$$15a^3 \cdot \dfrac{b^3}{20}a^4b^4=\dfrac{15a^7b^7}{20}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}15a^3\frac{b^3}{20}a^4b^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{15a^3b^3}{20}a^4b^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{15a^7b^3}{20}b^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{15a^7b^7}{20}\end{aligned} $$ | |
| ① | Multiply $15a^3$ by $ \dfrac{b^3}{20} $ to get $ \dfrac{ 15a^3b^3 }{ 20 } $. Step 1: Write $ 15a^3 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 15a^3 \cdot \frac{b^3}{20} & \xlongequal{\text{Step 1}} \frac{15a^3}{\color{red}{1}} \cdot \frac{b^3}{20} \xlongequal{\text{Step 2}} \frac{ 15a^3 \cdot b^3 }{ 1 \cdot 20 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 15a^3b^3 }{ 20 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{15a^3b^3}{20} $ by $ a^4 $ to get $ \dfrac{ 15a^7b^3 }{ 20 } $. Step 1: Write $ a^4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{15a^3b^3}{20} \cdot a^4 & \xlongequal{\text{Step 1}} \frac{15a^3b^3}{20} \cdot \frac{a^4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 15a^3b^3 \cdot a^4 }{ 20 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 15a^7b^3 }{ 20 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{15a^7b^3}{20} $ by $ b^4 $ to get $ \dfrac{ 15a^7b^7 }{ 20 } $. Step 1: Write $ b^4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{15a^7b^3}{20} \cdot b^4 & \xlongequal{\text{Step 1}} \frac{15a^7b^3}{20} \cdot \frac{b^4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 15a^7b^3 \cdot b^4 }{ 20 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 15a^7b^7 }{ 20 } \end{aligned} $$ |