Simplify ((x+2)^-9)/((x+2)^-5)

$\frac{{(x + 2)}^{- 9}}{{(x + 2)}^{- 5}}$

Step 1

Move ${(x + 2)}^{- 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(x + 2)}^{- 5} {(x + 2)}^{9}}$

Step 2

Multiply ${(x + 2)}^{- 5}$ by ${(x + 2)}^{9}$ by adding the exponents.

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

$\frac{1}{{(x + 2)}^{- 5 + 9}}$

Add $- 5$ and $9$ .

$\frac{1}{{(x + 2)}^{4}}$