$$7x^7 \cdot \dfrac{y^5}{2}x^6y^4=\dfrac{7x^{13}y^9}{2}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}7x^7\frac{y^5}{2}x^6y^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7x^7y^5}{2}x^6y^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{7x^{13}y^5}{2}y^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{7x^{13}y^9}{2}\end{aligned} $$ | |
| ① | Multiply $7x^7$ by $ \dfrac{y^5}{2} $ to get $ \dfrac{ 7x^7y^5 }{ 2 } $. Step 1: Write $ 7x^7 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 7x^7 \cdot \frac{y^5}{2} & \xlongequal{\text{Step 1}} \frac{7x^7}{\color{red}{1}} \cdot \frac{y^5}{2} \xlongequal{\text{Step 2}} \frac{ 7x^7 \cdot y^5 }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x^7y^5 }{ 2 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{7x^7y^5}{2} $ by $ x^6 $ to get $ \dfrac{ 7x^{13}y^5 }{ 2 } $. Step 1: Write $ x^6 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{7x^7y^5}{2} \cdot x^6 & \xlongequal{\text{Step 1}} \frac{7x^7y^5}{2} \cdot \frac{x^6}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7x^7y^5 \cdot x^6 }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x^{13}y^5 }{ 2 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{7x^{13}y^5}{2} $ by $ y^4 $ to get $ \dfrac{ 7x^{13}y^9 }{ 2 } $. 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. $$ \begin{aligned} \frac{7x^{13}y^5}{2} \cdot y^4 & \xlongequal{\text{Step 1}} \frac{7x^{13}y^5}{2} \cdot \frac{y^4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7x^{13}y^5 \cdot y^4 }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x^{13}y^9 }{ 2 } \end{aligned} $$ |