Simplify the Radical Expression (1/(m^-7*m^4))^(5/6)

${(\frac{1}{m^{- 7} \cdot m^{4}})}^{\frac{5}{6}}$

Multiply $m^{- 7}$ by $m^{4}$ by adding the exponents.

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

${(\frac{1}{m^{- 7 + 4}})}^{\frac{5}{6}}$

Add $- 7$ and $4$ .

${(\frac{1}{m^{- 3}})}^{\frac{5}{6}}$

Move $m^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(m^{3})}^{\frac{5}{6}}$

Multiply the exponents in ${(m^{3})}^{\frac{5}{6}}$ .

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

$m^{3 (\frac{5}{6})}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$m^{3 \frac{5}{3 (2)}}$

Cancel the common factor.

$m^{3 \frac{5}{3 \cdot 2}}$

Rewrite the expression.

$m^{\frac{5}{2}}$