Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}25x \cdot \frac{y^7}{25}xy^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{25xy^7}{25}xy^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{25x^2y^7}{25}y^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{25x^2y^{11}}{25}\end{aligned} $$ | |
| ① | Multiply $25x$ by $ \dfrac{y^7}{25} $ to get $ \dfrac{ 25xy^7 }{ 25 } $. Step 1: Write $ 25x $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 25x \cdot \frac{y^7}{25} & \xlongequal{\text{Step 1}} \frac{25x}{\color{red}{1}} \cdot \frac{y^7}{25} \xlongequal{\text{Step 2}} \frac{ 25x \cdot y^7 }{ 1 \cdot 25 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 25xy^7 }{ 25 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{25xy^7}{25} $ by $ x $ to get $ \dfrac{ 25x^2y^7 }{ 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. $$ \begin{aligned} \frac{25xy^7}{25} \cdot x & \xlongequal{\text{Step 1}} \frac{25xy^7}{25} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 25xy^7 \cdot x }{ 25 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 25x^2y^7 }{ 25 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{25x^2y^7}{25} $ by $ y^4 $ to get $ \dfrac{ 25x^2y^{11} }{ 25 } $. Step 1: Write $ y^4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{25x^2y^7}{25} \cdot y^4 & \xlongequal{\text{Step 1}} \frac{25x^2y^7}{25} \cdot \frac{y^4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 25x^2y^7 \cdot y^4 }{ 25 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 25x^2y^{11} }{ 25 } \end{aligned} $$ |