Simplify ((m^-1m^5)/(m^-2))^-3

${(\frac{m^{- 1} m^{5}}{m^{- 2}})}^{- 3}$

Step 1

Multiply $m^{- 1}$ by $m^{5}$ by adding the exponents.

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

${(\frac{m^{- 1 + 5}}{m^{- 2}})}^{- 3}$

Add $- 1$ and $5$ .

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

Step 2

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

${(m^{4} m^{2})}^{- 3}$

Step 3

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

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

${(m^{4 + 2})}^{- 3}$

Add $4$ and $2$ .

${(m^{6})}^{- 3}$

Step 4

Multiply the exponents in ${(m^{6})}^{- 3}$ .

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

$m^{6 \cdot - 3}$

Multiply $6$ by $- 3$ .

$m^{- 18}$

Step 5

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

$\frac{1}{m^{18}}$