Algebra Examples

$a^{3} b^{2} {(b^{- 1})}^{3}$

Step 1

Multiply the exponents in ${(b^{- 1})}^{3}$ .

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Step 1.1

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

$a^{3} b^{2} b^{- 1 \cdot 3}$

Step 1.2

Multiply $- 1$ by $3$ .

$a^{3} b^{2} b^{- 3}$

Step 2

Multiply $b^{2}$ by $b^{- 3}$ by adding the exponents.

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Step 2.1

Move $b^{- 3}$ .

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

Step 2.2

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

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

Step 2.3

Add $- 3$ and $2$ .

$a^{3} b^{- 1}$

Step 3

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

$a^{3} \frac{1}{b}$

Step 4

Combine $a^{3}$ and $\frac{1}{b}$ .

$\frac{a^{3}}{b}$