$$120x^3 \cdot \dfrac{y}{25}xy^5=\dfrac{120x^4y^6}{25}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}120x^3\frac{y}{25}xy^5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{120x^3y}{25}xy^5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{120x^4y}{25}y^5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{120x^4y^6}{25}\end{aligned} $$ | |
| ① | Multiply $120x^3$ by $ \dfrac{y}{25} $ to get $ \dfrac{ 120x^3y }{ 25 } $. Step 1: Write $ 120x^3 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 120x^3 \cdot \frac{y}{25} & \xlongequal{\text{Step 1}} \frac{120x^3}{\color{red}{1}} \cdot \frac{y}{25} \xlongequal{\text{Step 2}} \frac{ 120x^3 \cdot y }{ 1 \cdot 25 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 120x^3y }{ 25 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{120x^3y}{25} $ by $ x $ to get $ \dfrac{ 120x^4y }{ 25 } $. 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. $$ \begin{aligned} \frac{120x^3y}{25} \cdot x & \xlongequal{\text{Step 1}} \frac{120x^3y}{25} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 120x^3y \cdot x }{ 25 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 120x^4y }{ 25 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{120x^4y}{25} $ by $ y^5 $ to get $ \dfrac{ 120x^4y^6 }{ 25 } $. Step 1: Write $ y^5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{120x^4y}{25} \cdot y^5 & \xlongequal{\text{Step 1}} \frac{120x^4y}{25} \cdot \frac{y^5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 120x^4y \cdot y^5 }{ 25 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 120x^4y^6 }{ 25 } \end{aligned} $$ |