Question

Simplify the expression ${\left(8a^3\right)}^2{\left(2a\right)}^4$.

Short answer

The simplified form of the given expression is$1024a^{10}$.

Step-by-step solution

Step 1. Given information.

The given expression is${\left(8a^3\right)}^2{\left(2a\right)}^4$.

Step 2. Using the power of product property,

$$\begin{gathered} {\left(8a^3\right)}^2{\left(2a\right)}^4={\left(8\right)}^2{\left(a^3\right)}^2{\left(2\right)}^4{\left(a\right)}^4 \\ =64\times a^6\times 16\times a^4 \\ useproductproperty, \\ =1024a^{10} \end{gathered}$$