Simplify (a+b)^-3(a+b)^2(a+b)^-2

${(a + b)}^{- 3} {(a + b)}^{2} {(a + b)}^{- 2}$

Step 1

Multiply ${(a + b)}^{- 3}$ by ${(a + b)}^{2}$ by adding the exponents.

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

${(a + b)}^{- 3 + 2} {(a + b)}^{- 2}$

Add $- 3$ and $2$ .

${(a + b)}^{- 1} {(a + b)}^{- 2}$

Step 2

Multiply ${(a + b)}^{- 1}$ by ${(a + b)}^{- 2}$ by adding the exponents.

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

${(a + b)}^{- 1 - 2}$

Subtract $2$ from $- 1$ .

${(a + b)}^{- 3}$

Step 3

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

$\frac{1}{{(a + b)}^{3}}$