Simplify 16 root of (m^-5)/(m^-1)

$\sqrt[16]{\frac{m^{- 5}}{m^{- 1}}}$

Reduce the expression $\frac{m^{- 5}}{m^{- 1}}$ by cancelling the common factors.

Multiply by $1$ .

$\sqrt[16]{\frac{m^{- 5} \cdot 1}{m^{- 1}}}$

Factor $m^{- 5}$ out of $m^{- 1}$ .

$\sqrt[16]{\frac{m^{- 5} \cdot 1}{m^{- 5} m^{4}}}$

Cancel the common factor.

$\sqrt[16]{\frac{m^{- 5} \cdot 1}{m^{- 5} m^{4}}}$

Rewrite the expression.

$\sqrt[16]{\frac{1}{m^{4}}}$

Rewrite $1$ as $1^{4}$ .

$\sqrt[16]{\frac{1^{4}}{m^{4}}}$

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

$\sqrt[16]{{(\frac{1}{m})}^{4}}$

Rewrite $\sqrt[16]{{(\frac{1}{m})}^{4}}$ as $\sqrt[4]{\sqrt[4]{{(\frac{1}{m})}^{4}}}$ .

$\sqrt[4]{\sqrt[4]{{(\frac{1}{m})}^{4}}}$

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt[4]{\frac{1}{m}}$

Rewrite $\sqrt[4]{\frac{1}{m}}$ as $\frac{\sqrt[4]{1}}{\sqrt[4]{m}}$ .

$\frac{\sqrt[4]{1}}{\sqrt[4]{m}}$

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[4]{m}}$

Multiply $\frac{1}{\sqrt[4]{m}}$ by $\frac{{\sqrt[4]{m}}^{3}}{{\sqrt[4]{m}}^{3}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt[4]{m}}$ by $\frac{{\sqrt[4]{m}}^{3}}{{\sqrt[4]{m}}^{3}}$ .

$\frac{{\sqrt[4]{m}}^{3}}{\sqrt[4]{m} {\sqrt[4]{m}}^{3}}$

Raise $\sqrt[4]{m}$ to the power of $1$ .

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

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

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

Add $1$ and $3$ .

$\frac{{\sqrt[4]{m}}^{3}}{{\sqrt[4]{m}}^{4}}$

Rewrite ${\sqrt[4]{m}}^{4}$ as $m$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{m}$ as $m^{\frac{1}{4}}$ .

$\frac{{\sqrt[4]{m}}^{3}}{{(m^{\frac{1}{4}})}^{4}}$

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

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

Combine $\frac{1}{4}$ and $4$ .

$\frac{{\sqrt[4]{m}}^{3}}{m^{\frac{4}{4}}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{{\sqrt[4]{m}}^{3}}{m^{\frac{4}{4}}}$

Rewrite the expression.

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

Simplify.

$\frac{{\sqrt[4]{m}}^{3}}{m}$

Rewrite ${\sqrt[4]{m}}^{3}$ as ${(m^{3})}^{\frac{1}{4}}$ .

$\frac{\sqrt[4]{m^{3}}}{m}$

Simplify 16 root of (m^-5)/(m^-1)

Related Questions

Support LCMGCF.com by disabling your adblocker.