Answer
$$4{a^4}^2 \cdot \frac{a}{8a^{10}}=\frac{4a^9}{8a^{10}}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4{a^4}^2\frac{a}{8a^{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4\cdot1a^8\frac{a}{8a^{10}} \xlongequal{ } \\[1 em] & \xlongequal{ }4a^8\frac{a}{8a^{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4a^9}{8a^{10}}\end{aligned} $$ | |
| ① | $$ \left( a^4 \right)^2 = 1^2 \left( a^4 \right)^2 = a^8 $$ |
| ② | Multiply $4a^8$ by $ \dfrac{a}{8a^{10}} $ to get $ \dfrac{ 4a^9 }{ 8a^{10} } $. Step 1: Write $ 4a^8 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 4a^8 \cdot \frac{a}{8a^{10}} & \xlongequal{\text{Step 1}} \frac{4a^8}{\color{red}{1}} \cdot \frac{a}{8a^{10}} \xlongequal{\text{Step 2}} \frac{ 4a^8 \cdot a }{ 1 \cdot 8a^{10} } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4a^9 }{ 8a^{10} } \end{aligned} $$ |
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