Simplify ( fourth root of 2)^2

${(\sqrt[4]{2})}^{2}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{2}$ as $2^{\frac{1}{4}}$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2^{\frac{1}{2}}$

Step 5

Rewrite $2^{\frac{1}{2}}$ as $\sqrt{2}$ .

$\sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$