Simplify the Radical Expression sixth root of (t^-8)/(t^-4)

$\sqrt[6]{\frac{t^{- 8}}{t^{- 4}}}$

Reduce the expression $\frac{t^{- 8}}{t^{- 4}}$ by cancelling the common factors.

Multiply by $1$ .

$\sqrt[6]{\frac{t^{- 8} \cdot 1}{t^{- 4}}}$

Factor $t^{- 8}$ out of $t^{- 4}$ .

$\sqrt[6]{\frac{t^{- 8} \cdot 1}{t^{- 8} t^{4}}}$

Cancel the common factor.

$\sqrt[6]{\frac{t^{- 8} \cdot 1}{t^{- 8} t^{4}}}$

Rewrite the expression.

$\sqrt[6]{\frac{1}{t^{4}}}$

Rewrite $1$ as $1^{2}$ .

$\sqrt[6]{\frac{1^{2}}{t^{4}}}$

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

$\sqrt[6]{\frac{1^{2}}{{(t^{2})}^{2}}}$

Rewrite $\frac{1^{2}}{{(t^{2})}^{2}}$ as ${(\frac{1}{t^{2}})}^{2}$ .

$\sqrt[6]{{(\frac{1}{t^{2}})}^{2}}$

Rewrite $\sqrt[6]{{(\frac{1}{t^{2}})}^{2}}$ as $\sqrt[3]{\sqrt{{(\frac{1}{t^{2}})}^{2}}}$ .

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

Pull terms out from under the radical.

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

Remove non-negative terms from the absolute value.

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

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

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

Rewrite $\sqrt[3]{\frac{1}{t^{2}}}$ as $\frac{\sqrt[3]{1}}{\sqrt[3]{t^{2}}}$ .

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

Any root of $1$ is $1$ .

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

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

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

Combine and simplify the denominator.

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

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

Raise $\sqrt[3]{t^{2}}$ to the power of $1$ .

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

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

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

Add $1$ and $2$ .

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

Rewrite ${\sqrt[3]{t^{2}}}^{3}$ as $t^{2}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{t^{2}}$ as $t^{\frac{2}{3}}$ .

$\frac{{\sqrt[3]{t^{2}}}^{2}}{{(t^{\frac{2}{3}})}^{3}}$

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

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

Combine $\frac{2}{3}$ and $3$ .

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

Multiply $2$ by $3$ .

$\frac{{\sqrt[3]{t^{2}}}^{2}}{t^{\frac{6}{3}}}$

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2$ by $1$ .

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

Simplify the numerator.

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

$\frac{\sqrt[3]{{(t^{2})}^{2}}}{t^{2}}$

Multiply the exponents in ${(t^{2})}^{2}$ .

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

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

Multiply $2$ by $2$ .

$\frac{\sqrt[3]{t^{4}}}{t^{2}}$

Factor out $t^{3}$ .

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

Pull terms out from under the radical.

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

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

Factor $t$ out of $t \sqrt[3]{t}$ .

$\frac{t (\sqrt[3]{t})}{t^{2}}$

Cancel the common factors.

Factor $t$ out of $t^{2}$ .

$\frac{t (\sqrt[3]{t})}{t \cdot t}$

Cancel the common factor.

$\frac{t \sqrt[3]{t}}{t \cdot t}$

Rewrite the expression.

$\frac{\sqrt[3]{t}}{t}$

Simplify the Radical Expression sixth root of (t^-8)/(t^-4)

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