Simplify (a^3)/( square root of 15a^5)

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Algebra

$\frac{a^{3}}{\sqrt{15 a^{5}}}$

Simplify the denominator.

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Rewrite $15 a^{5}$ as ${(a^{2})}^{2} \cdot (15 a)$ .

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Factor out $a^{4}$ .

$\frac{a^{3}}{\sqrt{15 (a^{4} a)}}$

Rewrite $a^{4}$ as ${(a^{2})}^{2}$ .

$\frac{a^{3}}{\sqrt{15 ({(a^{2})}^{2} a)}}$

Reorder $15$ and ${(a^{2})}^{2}$ .

$\frac{a^{3}}{\sqrt{{(a^{2})}^{2} \cdot 15 a}}$

Add parentheses.

$\frac{a^{3}}{\sqrt{{(a^{2})}^{2} \cdot (15 a)}}$

Pull terms out from under the radical.

$\frac{a^{3}}{a^{2} \sqrt{15 a}}$

Cancel the common factor of $a^{3}$ and $a^{2}$ .

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Factor $a^{2}$ out of $a^{3}$ .

$\frac{a^{2} a}{a^{2} \sqrt{15 a}}$

Cancel the common factors.

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Factor $a^{2}$ out of $a^{2} \sqrt{15 a}$ .

$\frac{a^{2} a}{a^{2} (\sqrt{15 a})}$

Cancel the common factor.

$\frac{a^{2} a}{a^{2} \sqrt{15 a}}$

Rewrite the expression.

$\frac{a}{\sqrt{15 a}}$

Multiply $\frac{a}{\sqrt{15 a}}$ by $\frac{\sqrt{15 a}}{\sqrt{15 a}}$ .

$\frac{a}{\sqrt{15 a}} \cdot \frac{\sqrt{15 a}}{\sqrt{15 a}}$

Combine and simplify the denominator.

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Multiply $\frac{a}{\sqrt{15 a}}$ and $\frac{\sqrt{15 a}}{\sqrt{15 a}}$ .

$\frac{a \sqrt{15 a}}{\sqrt{15 a} \sqrt{15 a}}$

Raise $\sqrt{15 a}$ to the power of $1$ .

$\frac{a \sqrt{15 a}}{{\sqrt{15 a}}^{1} \sqrt{15 a}}$

Raise $\sqrt{15 a}$ to the power of $1$ .

$\frac{a \sqrt{15 a}}{{\sqrt{15 a}}^{1} {\sqrt{15 a}}^{1}}$

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

$\frac{a \sqrt{15 a}}{{\sqrt{15 a}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{a \sqrt{15 a}}{{\sqrt{15 a}}^{2}}$

Rewrite ${\sqrt{15 a}}^{2}$ as $15 a$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{15 a}$ as ${(15 a)}^{\frac{1}{2}}$ .

$\frac{a \sqrt{15 a}}{{({(15 a)}^{\frac{1}{2}})}^{2}}$

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

$\frac{a \sqrt{15 a}}{{(15 a)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{a \sqrt{15 a}}{{(15 a)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{a \sqrt{15 a}}{{(15 a)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{a \sqrt{15 a}}{{(15 a)}^{1}}$

Simplify.

$\frac{a \sqrt{15 a}}{15 a}$

Cancel the common factor of $a$ .

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Cancel the common factor.

$\frac{a \sqrt{15 a}}{15 a}$

Rewrite the expression.

$\frac{\sqrt{15 a}}{15}$

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