$$8\cdot\dfrac{a^3}{3}\cdot\dfrac{21}{12^8}=\dfrac{56a^3}{429981696}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}8 \cdot \frac{a^3}{3}\cdot\frac{21}{12^8}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8a^3}{3}\cdot\frac{21}{429981696} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{8a^3}{3} \cdot \frac{ 21 : \color{orangered}{ 3 } }{ 429981696 : \color{orangered}{ 3 }} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{8a^3}{3}\cdot\frac{7}{143327232} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{56a^3}{429981696}\end{aligned} $$ | |
| ① | Multiply $8$ by $ \dfrac{a^3}{3} $ to get $ \dfrac{ 8a^3 }{ 3 } $. Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 8 \cdot \frac{a^3}{3} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{a^3}{3} \xlongequal{\text{Step 2}} \frac{ 8 \cdot a^3 }{ 1 \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8a^3 }{ 3 } \end{aligned} $$ |
| ② | Multiply $8$ by $ \dfrac{a^3}{3} $ to get $ \dfrac{ 8a^3 }{ 3 } $. Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 8 \cdot \frac{a^3}{3} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{a^3}{3} \xlongequal{\text{Step 2}} \frac{ 8 \cdot a^3 }{ 1 \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8a^3 }{ 3 } \end{aligned} $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 3 } $. |
| ④ | Multiply $8$ by $ \dfrac{a^3}{3} $ to get $ \dfrac{ 8a^3 }{ 3 } $. Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 8 \cdot \frac{a^3}{3} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{a^3}{3} \xlongequal{\text{Step 2}} \frac{ 8 \cdot a^3 }{ 1 \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8a^3 }{ 3 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{8a^3}{3} $ by $ \dfrac{7}{143327232} $ to get $ \dfrac{ 56a^3 }{ 429981696 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{8a^3}{3} \cdot \frac{7}{143327232} & \xlongequal{\text{Step 1}} \frac{ 8a^3 \cdot 7 }{ 3 \cdot 143327232 } \xlongequal{\text{Step 2}} \frac{ 56a^3 }{ 429981696 } \end{aligned} $$ |