Simplify (1/( square root of 2))^2

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

Multiply $\frac{1}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Raise $\sqrt{2}$ to the power of $1$ .

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

Raise $\sqrt{2}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

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

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

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

$\frac{2}{4}$

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

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$

Simplify (1/( square root of 2))^2

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