Algebra Examples

$\frac{\sqrt{5 x}}{12}$

Multiply to rationalize the numerator.

$\frac{\sqrt{5 x} \sqrt{5 x}}{12 \sqrt{5 x}}$

Simplify.

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Raise $\sqrt{5 x}$ to the power of $1$ .

$\frac{{\sqrt{5 x}}^{1} \sqrt{5 x}}{12 \sqrt{5 x}}$

Raise $\sqrt{5 x}$ to the power of $1$ .

$\frac{{\sqrt{5 x}}^{1} {\sqrt{5 x}}^{1}}{12 \sqrt{5 x}}$

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

$\frac{{\sqrt{5 x}}^{1 + 1}}{12 \sqrt{5 x}}$

Add $1$ and $1$ .

$\frac{{\sqrt{5 x}}^{2}}{12 \sqrt{5 x}}$

Rewrite ${\sqrt{5 x}}^{2}$ as $5 x$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x}$ as ${(5 x)}^{\frac{1}{2}}$ .

$\frac{{({(5 x)}^{\frac{1}{2}})}^{2}}{12 \sqrt{5 x}}$

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

$\frac{{(5 x)}^{\frac{1}{2} \cdot 2}}{12 \sqrt{5 x}}$

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

$\frac{{(5 x)}^{\frac{2}{2}}}{12 \sqrt{5 x}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{{(5 x)}^{\frac{2}{2}}}{12 \sqrt{5 x}}$

Rewrite the expression.

$\frac{{(5 x)}^{1}}{12 \sqrt{5 x}}$

Simplify.

$\frac{5 x}{12 \sqrt{5 x}}$