Simplify x(2x)^2

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

Step 1

Apply the product rule to $2 x$ .

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

Step 2

Rewrite using the commutative property of multiplication.

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

Step 3

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

$2^{2} x^{3}$

Step 4

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

$4 x^{3}$