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