$$30x^6 \cdot \dfrac{y^5}{5}x^2y^3=\dfrac{30x^8y^8}{5}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}30x^6\frac{y^5}{5}x^2y^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{30x^6y^5}{5}x^2y^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{30x^8y^5}{5}y^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{30x^8y^8}{5}\end{aligned} $$ | |
| ① | Multiply $30x^6$ by $ \dfrac{y^5}{5} $ to get $ \dfrac{ 30x^6y^5 }{ 5 } $. Step 1: Write $ 30x^6 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 30x^6 \cdot \frac{y^5}{5} & \xlongequal{\text{Step 1}} \frac{30x^6}{\color{red}{1}} \cdot \frac{y^5}{5} \xlongequal{\text{Step 2}} \frac{ 30x^6 \cdot y^5 }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 30x^6y^5 }{ 5 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{30x^6y^5}{5} $ by $ x^2 $ to get $ \dfrac{ 30x^8y^5 }{ 5 } $. Step 1: Write $ x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{30x^6y^5}{5} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{30x^6y^5}{5} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 30x^6y^5 \cdot x^2 }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 30x^8y^5 }{ 5 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{30x^8y^5}{5} $ by $ y^3 $ to get $ \dfrac{ 30x^8y^8 }{ 5 } $. Step 1: Write $ y^3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{30x^8y^5}{5} \cdot y^3 & \xlongequal{\text{Step 1}} \frac{30x^8y^5}{5} \cdot \frac{y^3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 30x^8y^5 \cdot y^3 }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 30x^8y^8 }{ 5 } \end{aligned} $$ |