$$\dfrac{\dfrac{2}{5}xxyy}{\dfrac{4}{15}xxxxyyyyyyy}\dfrac{5}{3}xxyyy=\dfrac{150x^4y^5}{60x^4y^7}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{2}{5}xxyy}{\frac{4}{15}xxxxyyyyyyy}\frac{5}{3}xxyyy& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\frac{2x}{5}xyy}{\frac{4x}{15}xxxyyyyyyy}\frac{5x}{3}xyyy \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{\frac{2x^2}{5}yy}{\frac{4x^2}{15}xxyyyyyyy}\frac{5x^2}{3}yyy \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} \htmlClass{explanationCircle explanationCircle9}{\textcircled {9}} } }}}\frac{\frac{2x^2y}{5}y}{\frac{4x^3}{15}xyyyyyyy}\frac{5x^2y}{3}yy \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle10}{\textcircled {10}} \htmlClass{explanationCircle explanationCircle11}{\textcircled {11}} \htmlClass{explanationCircle explanationCircle12}{\textcircled {12}} } }}}\frac{\frac{2x^2y^2}{5}}{\frac{4x^4}{15}yyyyyyy}\frac{5x^2y^2}{3}y \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle13}{\textcircled {13}} \htmlClass{explanationCircle explanationCircle14}{\textcircled {14}} \htmlClass{explanationCircle explanationCircle15}{\textcircled {15}} } }}}\frac{\frac{2x^2y^2}{5}}{\frac{4x^4y}{15}yyyyyy}\frac{5x^2y^3}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle16}{\textcircled {16}} \htmlClass{explanationCircle explanationCircle17}{\textcircled {17}} \htmlClass{explanationCircle explanationCircle18}{\textcircled {18}} } }}}\frac{\frac{2x^2y^2}{5}}{\frac{4x^4y^2}{15}yyyyy}\frac{5x^2y^3}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle19}{\textcircled {19}} \htmlClass{explanationCircle explanationCircle20}{\textcircled {20}} \htmlClass{explanationCircle explanationCircle21}{\textcircled {21}} } }}}\frac{\frac{2x^2y^2}{5}}{\frac{4x^4y^3}{15}yyyy}\frac{5x^2y^3}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle22}{\textcircled {22}} \htmlClass{explanationCircle explanationCircle23}{\textcircled {23}} \htmlClass{explanationCircle explanationCircle24}{\textcircled {24}} } }}}\frac{\frac{2x^2y^2}{5}}{\frac{4x^4y^4}{15}yyy}\frac{5x^2y^3}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle25}{\textcircled {25}} \htmlClass{explanationCircle explanationCircle26}{\textcircled {26}} \htmlClass{explanationCircle explanationCircle27}{\textcircled {27}} } }}}\frac{\frac{2x^2y^2}{5}}{\frac{4x^4y^5}{15}yy}\frac{5x^2y^3}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle28}{\textcircled {28}} \htmlClass{explanationCircle explanationCircle29}{\textcircled {29}} \htmlClass{explanationCircle explanationCircle30}{\textcircled {30}} } }}}\frac{\frac{2x^2y^2}{5}}{\frac{4x^4y^6}{15}y}\frac{5x^2y^3}{3} \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle31}{\textcircled {31}} \htmlClass{explanationCircle explanationCircle32}{\textcircled {32}} \htmlClass{explanationCircle explanationCircle33}{\textcircled {33}} } }}}\frac{\frac{2x^2y^2}{5}}{\frac{4x^4y^7}{15}}\frac{5x^2y^3}{3} \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle34}{\textcircled {34}} \htmlClass{explanationCircle explanationCircle35}{\textcircled {35}} } }}}\frac{30x^2y^2}{20x^4y^7}\frac{5x^2y^3}{3} \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle36}{\textcircled {36}} } }}}\frac{150x^4y^5}{60x^4y^7}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{2}{5} $ by $ x $ to get $ \dfrac{ 2x }{ 5 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{2}{5} \cdot x & \xlongequal{\text{Step 1}} \frac{2}{5} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2 \cdot x }{ 5 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 2x }{ 5 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{4}{15} $ by $ x $ to get $ \dfrac{ 4x }{ 15 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4}{15} \cdot x & \xlongequal{\text{Step 1}} \frac{4}{15} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4 \cdot x }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x }{ 15 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{5}{3} $ by $ x $ to get $ \dfrac{ 5x }{ 3 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5}{3} \cdot x & \xlongequal{\text{Step 1}} \frac{5}{3} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x }{ 3 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 5x }{ 3 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{2x}{5} $ by $ x $ to get $ \dfrac{ 2x^2 }{ 5 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{2x}{5} \cdot x & \xlongequal{\text{Step 1}} \frac{2x}{5} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2x \cdot x }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^2 }{ 5 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{4x}{15} $ by $ x $ to get $ \dfrac{ 4x^2 }{ 15 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4x}{15} \cdot x & \xlongequal{\text{Step 1}} \frac{4x}{15} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4x \cdot x }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^2 }{ 15 } \end{aligned} $$ |
| ⑥ | Multiply $ \dfrac{5x}{3} $ by $ x $ to get $ \dfrac{ 5x^2 }{ 3 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x}{3} \cdot x & \xlongequal{\text{Step 1}} \frac{5x}{3} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x \cdot x }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2 }{ 3 } \end{aligned} $$ |
| ⑦ | Multiply $ \dfrac{2x^2}{5} $ by $ y $ to get $ \dfrac{ 2x^2y }{ 5 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{2x^2}{5} \cdot y & \xlongequal{\text{Step 1}} \frac{2x^2}{5} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2x^2 \cdot y }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^2y }{ 5 } \end{aligned} $$ |
| ⑧ | Multiply $ \dfrac{4x^2}{15} $ by $ x $ to get $ \dfrac{ 4x^3 }{ 15 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4x^2}{15} \cdot x & \xlongequal{\text{Step 1}} \frac{4x^2}{15} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4x^2 \cdot x }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^3 }{ 15 } \end{aligned} $$ |
| ⑨ | Multiply $ \dfrac{5x^2}{3} $ by $ y $ to get $ \dfrac{ 5x^2y }{ 3 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x^2}{3} \cdot y & \xlongequal{\text{Step 1}} \frac{5x^2}{3} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^2 \cdot y }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2y }{ 3 } \end{aligned} $$ |
| ⑩ | Multiply $ \dfrac{2x^2y}{5} $ by $ y $ to get $ \dfrac{ 2x^2y^2 }{ 5 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{2x^2y}{5} \cdot y & \xlongequal{\text{Step 1}} \frac{2x^2y}{5} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2x^2y \cdot y }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^2y^2 }{ 5 } \end{aligned} $$ |
| ⑪ | Multiply $ \dfrac{4x^3}{15} $ by $ x $ to get $ \dfrac{ 4x^4 }{ 15 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4x^3}{15} \cdot x & \xlongequal{\text{Step 1}} \frac{4x^3}{15} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4x^3 \cdot x }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^4 }{ 15 } \end{aligned} $$ |
| ⑫ | Multiply $ \dfrac{5x^2y}{3} $ by $ y $ to get $ \dfrac{ 5x^2y^2 }{ 3 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x^2y}{3} \cdot y & \xlongequal{\text{Step 1}} \frac{5x^2y}{3} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^2y \cdot y }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2y^2 }{ 3 } \end{aligned} $$ |
| ⑬ | Multiply $ \dfrac{2x^2y}{5} $ by $ y $ to get $ \dfrac{ 2x^2y^2 }{ 5 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{2x^2y}{5} \cdot y & \xlongequal{\text{Step 1}} \frac{2x^2y}{5} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2x^2y \cdot y }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^2y^2 }{ 5 } \end{aligned} $$ |
| ⑭ | Multiply $ \dfrac{4x^4}{15} $ by $ y $ to get $ \dfrac{ 4x^4y }{ 15 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4x^4}{15} \cdot y & \xlongequal{\text{Step 1}} \frac{4x^4}{15} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4x^4 \cdot y }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^4y }{ 15 } \end{aligned} $$ |
| ⑮ | Multiply $ \dfrac{5x^2y^2}{3} $ by $ y $ to get $ \dfrac{ 5x^2y^3 }{ 3 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x^2y^2}{3} \cdot y & \xlongequal{\text{Step 1}} \frac{5x^2y^2}{3} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^2y^2 \cdot y }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2y^3 }{ 3 } \end{aligned} $$ |
| ⑯ | Multiply $ \dfrac{2x^2y}{5} $ by $ y $ to get $ \dfrac{ 2x^2y^2 }{ 5 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{2x^2y}{5} \cdot y & \xlongequal{\text{Step 1}} \frac{2x^2y}{5} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2x^2y \cdot y }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^2y^2 }{ 5 } \end{aligned} $$ |
| ⑰ | Multiply $ \dfrac{4x^4y}{15} $ by $ y $ to get $ \dfrac{ 4x^4y^2 }{ 15 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4x^4y}{15} \cdot y & \xlongequal{\text{Step 1}} \frac{4x^4y}{15} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4x^4y \cdot y }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^4y^2 }{ 15 } \end{aligned} $$ |
| ⑱ | Multiply $ \dfrac{5x^2y^2}{3} $ by $ y $ to get $ \dfrac{ 5x^2y^3 }{ 3 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x^2y^2}{3} \cdot y & \xlongequal{\text{Step 1}} \frac{5x^2y^2}{3} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^2y^2 \cdot y }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2y^3 }{ 3 } \end{aligned} $$ |
| ⑲ | Multiply $ \dfrac{2x^2y}{5} $ by $ y $ to get $ \dfrac{ 2x^2y^2 }{ 5 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{2x^2y}{5} \cdot y & \xlongequal{\text{Step 1}} \frac{2x^2y}{5} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2x^2y \cdot y }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^2y^2 }{ 5 } \end{aligned} $$ |
| ⑳ | Multiply $ \dfrac{4x^4y^2}{15} $ by $ y $ to get $ \dfrac{ 4x^4y^3 }{ 15 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4x^4y^2}{15} \cdot y & \xlongequal{\text{Step 1}} \frac{4x^4y^2}{15} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4x^4y^2 \cdot y }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^4y^3 }{ 15 } \end{aligned} $$ |
| ⑴ | Multiply $ \dfrac{5x^2y^2}{3} $ by $ y $ to get $ \dfrac{ 5x^2y^3 }{ 3 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x^2y^2}{3} \cdot y & \xlongequal{\text{Step 1}} \frac{5x^2y^2}{3} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^2y^2 \cdot y }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2y^3 }{ 3 } \end{aligned} $$ |
| ⑵ | Multiply $ \dfrac{2x^2y}{5} $ by $ y $ to get $ \dfrac{ 2x^2y^2 }{ 5 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{2x^2y}{5} \cdot y & \xlongequal{\text{Step 1}} \frac{2x^2y}{5} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2x^2y \cdot y }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^2y^2 }{ 5 } \end{aligned} $$ |
| ⑶ | Multiply $ \dfrac{4x^4y^3}{15} $ by $ y $ to get $ \dfrac{ 4x^4y^4 }{ 15 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4x^4y^3}{15} \cdot y & \xlongequal{\text{Step 1}} \frac{4x^4y^3}{15} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4x^4y^3 \cdot y }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^4y^4 }{ 15 } \end{aligned} $$ |
| ⑷ | Multiply $ \dfrac{5x^2y^2}{3} $ by $ y $ to get $ \dfrac{ 5x^2y^3 }{ 3 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x^2y^2}{3} \cdot y & \xlongequal{\text{Step 1}} \frac{5x^2y^2}{3} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^2y^2 \cdot y }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2y^3 }{ 3 } \end{aligned} $$ |
| ⑸ | Multiply $ \dfrac{2x^2y}{5} $ by $ y $ to get $ \dfrac{ 2x^2y^2 }{ 5 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{2x^2y}{5} \cdot y & \xlongequal{\text{Step 1}} \frac{2x^2y}{5} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2x^2y \cdot y }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^2y^2 }{ 5 } \end{aligned} $$ |
| ⑹ | Multiply $ \dfrac{4x^4y^4}{15} $ by $ y $ to get $ \dfrac{ 4x^4y^5 }{ 15 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4x^4y^4}{15} \cdot y & \xlongequal{\text{Step 1}} \frac{4x^4y^4}{15} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4x^4y^4 \cdot y }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^4y^5 }{ 15 } \end{aligned} $$ |
| ⑺ | Multiply $ \dfrac{5x^2y^2}{3} $ by $ y $ to get $ \dfrac{ 5x^2y^3 }{ 3 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x^2y^2}{3} \cdot y & \xlongequal{\text{Step 1}} \frac{5x^2y^2}{3} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^2y^2 \cdot y }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2y^3 }{ 3 } \end{aligned} $$ |
| ⑻ | Multiply $ \dfrac{2x^2y}{5} $ by $ y $ to get $ \dfrac{ 2x^2y^2 }{ 5 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{2x^2y}{5} \cdot y & \xlongequal{\text{Step 1}} \frac{2x^2y}{5} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2x^2y \cdot y }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^2y^2 }{ 5 } \end{aligned} $$ |
| ⑼ | Multiply $ \dfrac{4x^4y^5}{15} $ by $ y $ to get $ \dfrac{ 4x^4y^6 }{ 15 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4x^4y^5}{15} \cdot y & \xlongequal{\text{Step 1}} \frac{4x^4y^5}{15} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4x^4y^5 \cdot y }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^4y^6 }{ 15 } \end{aligned} $$ |
| ⑽ | Multiply $ \dfrac{5x^2y^2}{3} $ by $ y $ to get $ \dfrac{ 5x^2y^3 }{ 3 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x^2y^2}{3} \cdot y & \xlongequal{\text{Step 1}} \frac{5x^2y^2}{3} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^2y^2 \cdot y }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2y^3 }{ 3 } \end{aligned} $$ |
| ⑾ | Multiply $ \dfrac{2x^2y}{5} $ by $ y $ to get $ \dfrac{ 2x^2y^2 }{ 5 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{2x^2y}{5} \cdot y & \xlongequal{\text{Step 1}} \frac{2x^2y}{5} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2x^2y \cdot y }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^2y^2 }{ 5 } \end{aligned} $$ |
| ⑿ | Multiply $ \dfrac{4x^4y^6}{15} $ by $ y $ to get $ \dfrac{ 4x^4y^7 }{ 15 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4x^4y^6}{15} \cdot y & \xlongequal{\text{Step 1}} \frac{4x^4y^6}{15} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4x^4y^6 \cdot y }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^4y^7 }{ 15 } \end{aligned} $$ |
| ⒀ | Multiply $ \dfrac{5x^2y^2}{3} $ by $ y $ to get $ \dfrac{ 5x^2y^3 }{ 3 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x^2y^2}{3} \cdot y & \xlongequal{\text{Step 1}} \frac{5x^2y^2}{3} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^2y^2 \cdot y }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2y^3 }{ 3 } \end{aligned} $$ |
| ⒁ | Divide $ \dfrac{2x^2y^2}{5} $ by $ \dfrac{4x^4y^7}{15} $ to get $ \dfrac{ 30x^2y^2 }{ 20x^4y^7 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{ \frac{2x^2y^2}{5} }{ \frac{\color{blue}{4x^4y^7}}{\color{blue}{15}} } & \xlongequal{\text{Step 1}} \frac{2x^2y^2}{5} \cdot \frac{\color{blue}{15}}{\color{blue}{4x^4y^7}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 2x^2y^2 \cdot 15 }{ 5 \cdot 4x^4y^7 } \xlongequal{\text{Step 3}} \frac{ 30x^2y^2 }{ 20x^4y^7 } \end{aligned} $$ |
| ⒂ | Multiply $ \dfrac{5x^2y^2}{3} $ by $ y $ to get $ \dfrac{ 5x^2y^3 }{ 3 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x^2y^2}{3} \cdot y & \xlongequal{\text{Step 1}} \frac{5x^2y^2}{3} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^2y^2 \cdot y }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2y^3 }{ 3 } \end{aligned} $$ |
| ⒃ | Multiply $ \dfrac{30x^2y^2}{20x^4y^7} $ by $ \dfrac{5x^2y^3}{3} $ to get $ \dfrac{ 150x^4y^5 }{ 60x^4y^7 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{30x^2y^2}{20x^4y^7} \cdot \frac{5x^2y^3}{3} & \xlongequal{\text{Step 1}} \frac{ 30x^2y^2 \cdot 5x^2y^3 }{ 20x^4y^7 \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 150x^4y^5 }{ 60x^4y^7 } \end{aligned} $$ |