$$12\cdot\dfrac{\dfrac{\dfrac{x^8}{5x^2y}}{3}}{2y^5}\cdot3\dfrac{y^4}{4x^2}=\dfrac{36x^8y^4}{120x^4y^6}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}12 \cdot \frac{\frac{\frac{x^8}{5x^2y}}{3}}{2y^5}\cdot3\frac{y^4}{4x^2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}12 \cdot \frac{\frac{x^8}{15x^2y}}{2y^5}\cdot3\frac{y^4}{4x^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}12 \cdot \frac{x^8}{30x^2y^6}\cdot3\frac{y^4}{4x^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{12x^8}{30x^2y^6}\cdot3\frac{y^4}{4x^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{36x^8}{30x^2y^6}\frac{y^4}{4x^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{36x^8y^4}{120x^4y^6}\end{aligned} $$ | |
| ① | Divide $ \dfrac{x^8}{5x^2y} $ by $ 3 $ to get $ \dfrac{ x^8 }{ 15x^2y } $. 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. $$ \begin{aligned} \frac{ \frac{x^8}{5x^2y} }{3} & \xlongequal{\text{Step 1}} \frac{x^8}{5x^2y} \cdot \frac{\color{blue}{1}}{\color{blue}{3}} \xlongequal{\text{Step 2}} \frac{ x^8 \cdot 1 }{ 5x^2y \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^8 }{ 15x^2y } \end{aligned} $$ |
| ② | Divide $ \dfrac{x^8}{15x^2y} $ by $ 2y^5 $ to get $ \dfrac{ x^8 }{ 30x^2y^6 } $. 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. $$ \begin{aligned} \frac{ \frac{x^8}{15x^2y} }{2y^5} & \xlongequal{\text{Step 1}} \frac{x^8}{15x^2y} \cdot \frac{\color{blue}{1}}{\color{blue}{2y^5}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ x^8 \cdot 1 }{ 15x^2y \cdot 2y^5 } \xlongequal{\text{Step 3}} \frac{ x^8 }{ 30x^2y^6 } \end{aligned} $$ |
| ③ | Multiply $12$ by $ \dfrac{x^8}{30x^2y^6} $ to get $ \dfrac{ 12x^8 }{ 30x^2y^6 } $. Step 1: Write $ 12 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 12 \cdot \frac{x^8}{30x^2y^6} & \xlongequal{\text{Step 1}} \frac{12}{\color{red}{1}} \cdot \frac{x^8}{30x^2y^6} \xlongequal{\text{Step 2}} \frac{ 12 \cdot x^8 }{ 1 \cdot 30x^2y^6 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12x^8 }{ 30x^2y^6 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{12x^8}{30x^2y^6} $ by $ 3 $ to get $ \dfrac{ 36x^8 }{ 30x^2y^6 } $. Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{12x^8}{30x^2y^6} \cdot 3 & \xlongequal{\text{Step 1}} \frac{12x^8}{30x^2y^6} \cdot \frac{3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 12x^8 \cdot 3 }{ 30x^2y^6 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 36x^8 }{ 30x^2y^6 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{36x^8}{30x^2y^6} $ by $ \dfrac{y^4}{4x^2} $ to get $ \dfrac{ 36x^8y^4 }{ 120x^4y^6 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{36x^8}{30x^2y^6} \cdot \frac{y^4}{4x^2} & \xlongequal{\text{Step 1}} \frac{ 36x^8 \cdot y^4 }{ 30x^2y^6 \cdot 4x^2 } \xlongequal{\text{Step 2}} \frac{ 36x^8y^4 }{ 120x^4y^6 } \end{aligned} $$ |