Simplify (4a^3)^2a^5

${(4 a^{3})}^{2} a^{5}$

Step 1

Apply the product rule to $4 a^{3}$ .

$4^{2} {(a^{3})}^{2} a^{5}$

Step 2

Raise $4$ to the power of $2$ .

$16 {(a^{3})}^{2} a^{5}$

Step 3

Multiply the exponents in ${(a^{3})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$16 a^{3 \cdot 2} a^{5}$

Multiply $3$ by $2$ .

$16 a^{6} a^{5}$

Step 4

Multiply $a^{6}$ by $a^{5}$ by adding the exponents.

Move $a^{5}$ .

$16 (a^{5} a^{6})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$16 a^{5 + 6}$

Add $5$ and $6$ .

$16 a^{11}$