$$15x^2 \cdot \dfrac{y^3}{y}\dfrac{b^2}{5}x^4\dfrac{y^2}{14}b^5=\dfrac{15b^7x^6y^5}{70y}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}15x^2\frac{y^3}{y}\frac{b^2}{5}x^4\frac{y^2}{14}b^5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{15x^2y^3}{y}\frac{b^2}{5}x^4\frac{y^2}{14}b^5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{15b^2x^2y^3}{5y}x^4\frac{y^2}{14}b^5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{15b^2x^6y^3}{5y}\frac{y^2}{14}b^5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{15b^2x^6y^5}{70y}b^5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{15b^7x^6y^5}{70y}\end{aligned} $$ | |
| ① | Multiply $15x^2$ by $ \dfrac{y^3}{y} $ to get $ \dfrac{ 15x^2y^3 }{ y } $. Step 1: Write $ 15x^2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 15x^2 \cdot \frac{y^3}{y} & \xlongequal{\text{Step 1}} \frac{15x^2}{\color{red}{1}} \cdot \frac{y^3}{y} \xlongequal{\text{Step 2}} \frac{ 15x^2 \cdot y^3 }{ 1 \cdot y } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 15x^2y^3 }{ y } \end{aligned} $$ |
| ② | Multiply $ \dfrac{15x^2y^3}{y} $ by $ \dfrac{b^2}{5} $ to get $ \dfrac{ 15b^2x^2y^3 }{ 5y } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{15x^2y^3}{y} \cdot \frac{b^2}{5} & \xlongequal{\text{Step 1}} \frac{ 15x^2y^3 \cdot b^2 }{ y \cdot 5 } \xlongequal{\text{Step 2}} \frac{ 15b^2x^2y^3 }{ 5y } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{15b^2x^2y^3}{5y} $ by $ x^4 $ to get $ \dfrac{ 15b^2x^6y^3 }{ 5y } $. Step 1: Write $ x^4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{15b^2x^2y^3}{5y} \cdot x^4 & \xlongequal{\text{Step 1}} \frac{15b^2x^2y^3}{5y} \cdot \frac{x^4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 15b^2x^2y^3 \cdot x^4 }{ 5y \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 15b^2x^6y^3 }{ 5y } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{15b^2x^6y^3}{5y} $ by $ \dfrac{y^2}{14} $ to get $ \dfrac{ 15b^2x^6y^5 }{ 70y } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{15b^2x^6y^3}{5y} \cdot \frac{y^2}{14} & \xlongequal{\text{Step 1}} \frac{ 15b^2x^6y^3 \cdot y^2 }{ 5y \cdot 14 } \xlongequal{\text{Step 2}} \frac{ 15b^2x^6y^5 }{ 70y } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{15b^2x^6y^5}{70y} $ by $ b^5 $ to get $ \dfrac{ 15b^7x^6y^5 }{ 70y } $. Step 1: Write $ b^5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{15b^2x^6y^5}{70y} \cdot b^5 & \xlongequal{\text{Step 1}} \frac{15b^2x^6y^5}{70y} \cdot \frac{b^5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 15b^2x^6y^5 \cdot b^5 }{ 70y \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 15b^7x^6y^5 }{ 70y } \end{aligned} $$ |