$$24a^2 \cdot \dfrac{b^8}{8}a^2b^5=\dfrac{24a^4b^{13}}{8}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}24a^2\frac{b^8}{8}a^2b^5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{24a^2b^8}{8}a^2b^5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{24a^4b^8}{8}b^5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{24a^4b^{13}}{8}\end{aligned} $$ | |
| ① | Multiply $24a^2$ by $ \dfrac{b^8}{8} $ to get $ \dfrac{ 24a^2b^8 }{ 8 } $. Step 1: Write $ 24a^2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 24a^2 \cdot \frac{b^8}{8} & \xlongequal{\text{Step 1}} \frac{24a^2}{\color{red}{1}} \cdot \frac{b^8}{8} \xlongequal{\text{Step 2}} \frac{ 24a^2 \cdot b^8 }{ 1 \cdot 8 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 24a^2b^8 }{ 8 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{24a^2b^8}{8} $ by $ a^2 $ to get $ \dfrac{ 24a^4b^8 }{ 8 } $. Step 1: Write $ a^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{24a^2b^8}{8} \cdot a^2 & \xlongequal{\text{Step 1}} \frac{24a^2b^8}{8} \cdot \frac{a^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 24a^2b^8 \cdot a^2 }{ 8 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 24a^4b^8 }{ 8 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{24a^4b^8}{8} $ by $ b^5 $ to get $ \dfrac{ 24a^4b^{13} }{ 8 } $. Step 1: Write $ b^5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{24a^4b^8}{8} \cdot b^5 & \xlongequal{\text{Step 1}} \frac{24a^4b^8}{8} \cdot \frac{b^5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 24a^4b^8 \cdot b^5 }{ 8 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 24a^4b^{13} }{ 8 } \end{aligned} $$ |