Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5x^6\frac{y^{12}}{10}x^7y^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5x^6y^{12}}{10}x^7y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5x^{13}y^{12}}{10}y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{5x^{13}y^{14}}{10}\end{aligned} $$ | |
| ① | Multiply $5x^6$ by $ \dfrac{y^{12}}{10} $ to get $ \dfrac{ 5x^6y^{12} }{ 10 } $. Step 1: Write $ 5x^6 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 5x^6 \cdot \frac{y^{12}}{10} & \xlongequal{\text{Step 1}} \frac{5x^6}{\color{red}{1}} \cdot \frac{y^{12}}{10} \xlongequal{\text{Step 2}} \frac{ 5x^6 \cdot y^{12} }{ 1 \cdot 10 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^6y^{12} }{ 10 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{5x^6y^{12}}{10} $ by $ x^7 $ to get $ \dfrac{ 5x^{13}y^{12} }{ 10 } $. 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. $$ \begin{aligned} \frac{5x^6y^{12}}{10} \cdot x^7 & \xlongequal{\text{Step 1}} \frac{5x^6y^{12}}{10} \cdot \frac{x^7}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^6y^{12} \cdot x^7 }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^{13}y^{12} }{ 10 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{5x^{13}y^{12}}{10} $ by $ y^2 $ to get $ \dfrac{ 5x^{13}y^{14} }{ 10 } $. Step 1: Write $ y^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x^{13}y^{12}}{10} \cdot y^2 & \xlongequal{\text{Step 1}} \frac{5x^{13}y^{12}}{10} \cdot \frac{y^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^{13}y^{12} \cdot y^2 }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^{13}y^{14} }{ 10 } \end{aligned} $$ |