Simplify (k^4m^2)/(k^-2(m^-2)^-4)

$\frac{k^{4} m^{2}}{k^{- 2} {(m^{- 2})}^{- 4}}$

Step 1

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

$\frac{k^{4} m^{2} k^{2}}{{(m^{- 2})}^{- 4}}$

Step 2

Move ${(m^{- 2})}^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$k^{4} m^{2} k^{2} {(m^{- 2})}^{4}$

Step 3

Multiply $k^{4}$ by $k^{2}$ by adding the exponents.

Move $k^{2}$ .

$k^{2} k^{4} m^{2} {(m^{- 2})}^{4}$

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

$k^{2 + 4} m^{2} {(m^{- 2})}^{4}$

Add $2$ and $4$ .

$k^{6} m^{2} {(m^{- 2})}^{4}$

Step 4

Multiply the exponents in ${(m^{- 2})}^{4}$ .

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

$k^{6} m^{2} m^{- 2 \cdot 4}$

Multiply $- 2$ by $4$ .

$k^{6} m^{2} m^{- 8}$

Step 5

Multiply $m^{2}$ by $m^{- 8}$ by adding the exponents.

Move $m^{- 8}$ .

$k^{6} (m^{- 8} m^{2})$

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

$k^{6} m^{- 8 + 2}$

Add $- 8$ and $2$ .

$k^{6} m^{- 6}$

Step 6

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

$k^{6} \frac{1}{m^{6}}$

Step 7

Combine $k^{6}$ and $\frac{1}{m^{6}}$ .

$\frac{k^{6}}{m^{6}}$