Simplify ((x+y)^-2(x+y)^4)/((x+y)^3)

$\frac{{(x + y)}^{- 2} {(x + y)}^{4}}{{(x + y)}^{3}}$

Step 1

Multiply ${(x + y)}^{- 2}$ by ${(x + y)}^{4}$ by adding the exponents.

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

$\frac{{(x + y)}^{- 2 + 4}}{{(x + y)}^{3}}$

Add $- 2$ and $4$ .

$\frac{{(x + y)}^{2}}{{(x + y)}^{3}}$

Step 2

Cancel the common factor of ${(x + y)}^{2}$ and ${(x + y)}^{3}$ .

Multiply by $1$ .

$\frac{{(x + y)}^{2} \cdot 1}{{(x + y)}^{3}}$

Cancel the common factors.

Factor ${(x + y)}^{2}$ out of ${(x + y)}^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x + y}$