Answer
$$8x^3 \cdot \frac{y^4}{20^7}y^7=\frac{8x^3y^{11}}{1280000000}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}8x^3\frac{y^4}{20^7}y^7& \xlongequal{ }8x^3\frac{y^4}{1280000000}y^7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8x^3y^4}{1280000000}y^7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{8x^3y^{11}}{1280000000}\end{aligned} $$ | |
| ① | Multiply $8x^3$ by $ \dfrac{y^4}{1280000000} $ to get $ \dfrac{ 8x^3y^4 }{ 1280000000 } $. Step 1: Write $ 8x^3 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 8x^3 \cdot \frac{y^4}{1280000000} & \xlongequal{\text{Step 1}} \frac{8x^3}{\color{red}{1}} \cdot \frac{y^4}{1280000000} \xlongequal{\text{Step 2}} \frac{ 8x^3 \cdot y^4 }{ 1 \cdot 1280000000 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8x^3y^4 }{ 1280000000 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{8x^3y^4}{1280000000} $ by $ y^7 $ to get $ \dfrac{ 8x^3y^{11} }{ 1280000000 } $. Step 1: Write $ y^7 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{8x^3y^4}{1280000000} \cdot y^7 & \xlongequal{\text{Step 1}} \frac{8x^3y^4}{1280000000} \cdot \frac{y^7}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 8x^3y^4 \cdot y^7 }{ 1280000000 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 8x^3y^{11} }{ 1280000000 } \end{aligned} $$ |
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