Simplify cube root of (x^6)/(x^10)

$\sqrt[3]{\frac{x^{6}}{x^{10}}}$

Reduce the expression $\frac{x^{6}}{x^{10}}$ by cancelling the common factors.

Multiply by $1$ .

$\sqrt[3]{\frac{x^{6} \cdot 1}{x^{10}}}$

Factor $x^{6}$ out of $x^{10}$ .

$\sqrt[3]{\frac{x^{6} \cdot 1}{x^{6} x^{4}}}$

Cancel the common factor.

$\sqrt[3]{\frac{x^{6} \cdot 1}{x^{6} x^{4}}}$

Rewrite the expression.

$\sqrt[3]{\frac{1}{x^{4}}}$

Rewrite $\frac{1}{x^{4}}$ as ${(\frac{1}{x})}^{3} \frac{1}{x}$ .

Factor the perfect power $1^{3}$ out of $1$ .

$\sqrt[3]{\frac{1^{3} \cdot 1}{x^{4}}}$

Factor the perfect power $x^{3}$ out of $x^{4}$ .

$\sqrt[3]{\frac{1^{3} \cdot 1}{x^{3} x}}$

Rearrange the fraction $\frac{1^{3} \cdot 1}{x^{3} x}$ .

$\sqrt[3]{{(\frac{1}{x})}^{3} \frac{1}{x}}$

Pull terms out from under the radical.

$\frac{1}{x} \sqrt[3]{\frac{1}{x}}$

Rewrite $\sqrt[3]{\frac{1}{x}}$ as $\frac{\sqrt[3]{1}}{\sqrt[3]{x}}$ .

$\frac{1}{x} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{x}}$

Any root of $1$ is $1$ .

$\frac{1}{x} \cdot \frac{1}{\sqrt[3]{x}}$

Multiply $\frac{1}{\sqrt[3]{x}}$ by $\frac{{\sqrt[3]{x}}^{2}}{{\sqrt[3]{x}}^{2}}$ .

$\frac{1}{x} (\frac{1}{\sqrt[3]{x}} \cdot \frac{{\sqrt[3]{x}}^{2}}{{\sqrt[3]{x}}^{2}})$

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt[3]{x}}$ by $\frac{{\sqrt[3]{x}}^{2}}{{\sqrt[3]{x}}^{2}}$ .

$\frac{1}{x} \cdot \frac{{\sqrt[3]{x}}^{2}}{\sqrt[3]{x} {\sqrt[3]{x}}^{2}}$

Raise $\sqrt[3]{x}$ to the power of $1$ .

$\frac{1}{x} \cdot \frac{{\sqrt[3]{x}}^{2}}{{\sqrt[3]{x}}^{1} {\sqrt[3]{x}}^{2}}$

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

$\frac{1}{x} \cdot \frac{{\sqrt[3]{x}}^{2}}{{\sqrt[3]{x}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{1}{x} \cdot \frac{{\sqrt[3]{x}}^{2}}{{\sqrt[3]{x}}^{3}}$

Rewrite ${\sqrt[3]{x}}^{3}$ as $x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x}$ as $x^{\frac{1}{3}}$ .

$\frac{1}{x} \cdot \frac{{\sqrt[3]{x}}^{2}}{{(x^{\frac{1}{3}})}^{3}}$

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

$\frac{1}{x} \cdot \frac{{\sqrt[3]{x}}^{2}}{x^{\frac{1}{3} \cdot 3}}$

Combine $\frac{1}{3}$ and $3$ .

$\frac{1}{x} \cdot \frac{{\sqrt[3]{x}}^{2}}{x^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{1}{x} \cdot \frac{{\sqrt[3]{x}}^{2}}{x^{\frac{3}{3}}}$

Rewrite the expression.

$\frac{1}{x} \cdot \frac{{\sqrt[3]{x}}^{2}}{x^{1}}$

Simplify.

$\frac{1}{x} \cdot \frac{{\sqrt[3]{x}}^{2}}{x}$

Combine.

$\frac{1 {\sqrt[3]{x}}^{2}}{x \cdot x}$

Simplify the expression.

Multiply $x$ by $x$ .

$\frac{1 {\sqrt[3]{x}}^{2}}{x^{2}}$

Multiply ${\sqrt[3]{x}}^{2}$ by $1$ .

$\frac{{\sqrt[3]{x}}^{2}}{x^{2}}$

Rewrite ${\sqrt[3]{x}}^{2}$ as ${(x^{2})}^{\frac{1}{3}}$ .

$\frac{\sqrt[3]{x^{2}}}{x^{2}}$

Simplify cube root of (x^6)/(x^10)

Related Questions

Support LCMGCF.com by disabling your adblocker.