Find the Exact Value ( square root of 2)^2

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$2^{1}$

Step 5

Evaluate the exponent.

$2$