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