Simplify fifth root of 1/(m^7*m^8)

$\sqrt[5]{\frac{1}{m^{7} \cdot m^{8}}}$

Multiply $m^{7}$ by $m^{8}$ by adding the exponents.

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

$\sqrt[5]{\frac{1}{m^{7 + 8}}}$

Add $7$ and $8$ .

$\sqrt[5]{\frac{1}{m^{15}}}$

Rewrite $1$ as $1^{5}$ .

$\sqrt[5]{\frac{1^{5}}{m^{15}}}$

Rewrite $m^{15}$ as ${(m^{3})}^{5}$ .

$\sqrt[5]{\frac{1^{5}}{{(m^{3})}^{5}}}$

Rewrite $\frac{1^{5}}{{(m^{3})}^{5}}$ as ${(\frac{1}{m^{3}})}^{5}$ .

$\sqrt[5]{{(\frac{1}{m^{3}})}^{5}}$

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

$\frac{1}{m^{3}}$