Algebra Examples

$\frac{{(a + b)}^{3} {(a - b)}^{- 2}}{{(a + b)}^{2} {(a - b)}^{0}}$

Step 1

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

$\frac{{(a + b)}^{3}}{{(a + b)}^{2} {(a - b)}^{0} {(a - b)}^{2}}$

Step 2

Multiply ${(a - b)}^{0}$ by ${(a - b)}^{2}$ by adding the exponents.

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Step 2.1

Move ${(a - b)}^{2}$ .

$\frac{{(a + b)}^{3}}{{(a + b)}^{2} ({(a - b)}^{2} {(a - b)}^{0})}$

Step 2.2

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

$\frac{{(a + b)}^{3}}{{(a + b)}^{2} {(a - b)}^{2 + 0}}$

Step 2.3

Add $2$ and $0$ .

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

Step 3

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

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Step 3.1

Factor ${(a + b)}^{2}$ out of ${(a + b)}^{3}$ .

$\frac{{(a + b)}^{2} (a + b)}{{(a + b)}^{2} {(a - b)}^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor ${(a + b)}^{2}$ out of ${(a + b)}^{2} {(a - b)}^{2}$ .

$\frac{{(a + b)}^{2} (a + b)}{{(a + b)}^{2} ({(a - b)}^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{{(a + b)}^{2} (a + b)}{{(a + b)}^{2} {(a - b)}^{2}}$

Step 3.2.3

Rewrite the expression.

$\frac{a + b}{{(a - b)}^{2}}$