Simplify (k^5m^2)/(k^-2(m^-2)^-5)

$\frac{k^{5} m^{2}}{k^{- 2} {(m^{- 2})}^{- 5}}$

Move $k^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{k^{5} m^{2} k^{2}}{{(m^{- 2})}^{- 5}}$

Move ${(m^{- 2})}^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$k^{5} m^{2} k^{2} {(m^{- 2})}^{5}$

Multiply $k^{5}$ by $k^{2}$ by adding the exponents.

Move $k^{2}$ .

$k^{2} k^{5} m^{2} {(m^{- 2})}^{5}$

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

$k^{2 + 5} m^{2} {(m^{- 2})}^{5}$

Add $2$ and $5$ .

$k^{7} m^{2} {(m^{- 2})}^{5}$

Multiply the exponents in ${(m^{- 2})}^{5}$ .

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

$k^{7} m^{2} m^{- 2 \cdot 5}$

Multiply $- 2$ by $5$ .

$k^{7} m^{2} m^{- 10}$

Multiply $m^{2}$ by $m^{- 10}$ by adding the exponents.

Move $m^{- 10}$ .

$k^{7} (m^{- 10} m^{2})$

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

$k^{7} m^{- 10 + 2}$

Add $- 10$ and $2$ .

$k^{7} m^{- 8}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$k^{7} \frac{1}{m^{8}}$

Combine $k^{7}$ and $\frac{1}{m^{8}}$ .

$\frac{k^{7}}{m^{8}}$