Simplify 2(2x^2)^2

$2 {(2 x^{2})}^{2}$

Step 1

Apply the product rule to $2 x^{2}$ .

$2 (2^{2} {(x^{2})}^{2})$

Step 2

Multiply $2$ by $2^{2}$ by adding the exponents.

Move $2^{2}$ .

$2^{2} \cdot 2 {(x^{2})}^{2}$

Multiply $2^{2}$ by $2$ .

Raise $2$ to the power of $1$ .

$2^{2} \cdot 2^{1} {(x^{2})}^{2}$

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

$2^{2 + 1} {(x^{2})}^{2}$

Add $2$ and $1$ .

$2^{3} {(x^{2})}^{2}$

Step 3

Raise $2$ to the power of $3$ .

$8 {(x^{2})}^{2}$

Step 4

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

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

$8 x^{2 \cdot 2}$

Multiply $2$ by $2$ .

$8 x^{4}$