Simplify the Radical Expression 1/( square root of x^5)

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

Step 1

Simplify the denominator.

Rewrite $x^{5}$ as ${(x^{2})}^{2} x$ .

Factor out $x^{4}$ .

$\frac{1}{\sqrt{x^{4} x}}$

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

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

Pull terms out from under the radical.

$\frac{1}{| x^{2} | \sqrt{x}}$

Remove non-negative terms from the absolute value.

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

Step 2

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

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

Step 3

Combine and simplify the denominator.

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

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

Move $\sqrt{x}$ .

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

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

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

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

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

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

$\frac{\sqrt{x}}{x^{2} {\sqrt{x}}^{1 + 1}}$

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 4

Multiply $x^{2}$ by $x$ by adding the exponents.

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

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

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

$\frac{\sqrt{x}}{x^{2 + 1}}$

Add $2$ and $1$ .

$\frac{\sqrt{x}}{x^{3}}$

Simplify the Radical Expression 1/( square root of x^5)

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