Simplify ((2m)^-2n^5)/(-m^4n^-3)

$\frac{{(2 m)}^{- 2} n^{5}}{- m^{4} n^{- 3}}$

Step 1

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

$\frac{n^{5}}{- m^{4} n^{- 3} {(2 m)}^{2}}$

Step 2

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

$\frac{n^{5} n^{3}}{- m^{4} {(2 m)}^{2}}$

Step 3

Multiply $n^{5}$ by $n^{3}$ by adding the exponents.

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

$\frac{n^{5 + 3}}{- m^{4} {(2 m)}^{2}}$

Add $5$ and $3$ .

$\frac{n^{8}}{- m^{4} {(2 m)}^{2}}$

Step 4

Simplify the denominator.

Apply the product rule to $2 m$ .

$\frac{n^{8}}{- m^{4} \cdot 2^{2} m^{2}}$

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

Move $m^{2}$ .

$\frac{n^{8}}{- (m^{2} m^{4}) \cdot 2^{2}}$

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

$\frac{n^{8}}{- m^{2 + 4} \cdot 2^{2}}$

Add $2$ and $4$ .

$\frac{n^{8}}{- m^{6} \cdot 2^{2}}$

Raise $2$ to the power of $2$ .

$\frac{n^{8}}{- m^{6} \cdot 4}$

Multiply $4$ by $- 1$ .

$\frac{n^{8}}{- 4 m^{6}}$

Step 5

Move the negative in front of the fraction.

$- \frac{n^{8}}{4 m^{6}}$