Simplify ( square root of 2x^2)^4

${(\sqrt{2 x^{2}})}^{4}$

Step 1

Reorder $2$ and $x^{2}$ .

${\sqrt{x^{2} \cdot 2}}^{4}$

Step 2

Pull terms out from under the radical.

${(x \sqrt{2})}^{4}$

Step 3

Apply the product rule to $x \sqrt{2}$ .

$x^{4} {\sqrt{2}}^{4}$

Step 4

Rewrite ${\sqrt{2}}^{4}$ as $2^{2}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$x^{4} {(2^{\frac{1}{2}})}^{4}$

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

$x^{4} \cdot 2^{\frac{1}{2} \cdot 4}$

Combine $\frac{1}{2}$ and $4$ .

$x^{4} \cdot 2^{\frac{4}{2}}$

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4$ .

$x^{4} \cdot 2^{\frac{2 \cdot 2}{2}}$

Cancel the common factors.

Factor $2$ out of $2$ .

$x^{4} \cdot 2^{\frac{2 \cdot 2}{2 (1)}}$

Cancel the common factor.

$x^{4} \cdot 2^{\frac{2 \cdot 2}{2 \cdot 1}}$

Rewrite the expression.

$x^{4} \cdot 2^{\frac{2}{1}}$

Divide $2$ by $1$ .

$x^{4} \cdot 2^{2}$

Step 5

Simplify the expression.

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

$x^{4} \cdot 4$

Move $4$ to the left of $x^{4}$ .

$4 x^{4}$