Basic Math Examples

$\frac{1}{2} \cdot {(\sqrt{130})}^{2}$

Step 1

Rewrite ${\sqrt{130}}^{2}$ as $130$ .

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Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{130}$ as $130^{\frac{1}{2}}$ .

$\frac{1}{2} \cdot {(130^{\frac{1}{2}})}^{2}$

Step 1.2

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

$\frac{1}{2} \cdot 130^{\frac{1}{2} \cdot 2}$

Step 1.3

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

$\frac{1}{2} \cdot 130^{\frac{2}{2}}$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Cancel the common factor.

$\frac{1}{2} \cdot 130^{\frac{2}{2}}$

Step 1.4.2

Rewrite the expression.

$\frac{1}{2} \cdot 130^{1}$

Step 1.5

Evaluate the exponent.

$\frac{1}{2} \cdot 130$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $130$ .

$\frac{1}{2} \cdot (2 (65))$

Step 2.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 65)$

Step 2.3

Rewrite the expression.

$65$