Pre-Algebra Examples

${(\sqrt{5})}^{2}$

Step 1

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt{5}$ as

$5^{\frac{1}{2}}$ .

${(5^{\frac{1}{2}})}^{2}$

Step 2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$5^{\frac{1}{2} \cdot 2}$

Step 3

Combine

$\frac{1}{2}$ and

$2$ .

$5^{\frac{2}{2}}$

Step 4

Cancel the common factor of

$2$ .

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Step 4.1

Cancel the common factor.

$5^{\frac{2}{2}}$

Step 4.2

Rewrite the expression.

$5^{1}$

$5^{1}$

Step 5

Evaluate the exponent.

$5$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$