Simplify a^3*(a^2b)^4

$a^{3} \cdot {(a^{2} b)}^{4}$

Step 1

Apply the product rule to $a^{2} b$ .

$a^{3} \cdot ({(a^{2})}^{4} b^{4})$

Step 2

Multiply the exponents in ${(a^{2})}^{4}$ .

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

$a^{3} \cdot (a^{2 \cdot 4} b^{4})$

Multiply $2$ by $4$ .

$a^{3} \cdot (a^{8} b^{4})$

Step 3

Multiply $a^{3}$ by $a^{8}$ by adding the exponents.

Move $a^{8}$ .

$a^{8} a^{3} \cdot b^{4}$

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

$a^{8 + 3} \cdot b^{4}$

Add $8$ and $3$ .

$a^{11} \cdot b^{4}$

$a^{11} b^{4}$