Algebra Examples

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

Step 1

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

$b^{3} {(3 \frac{1}{b})}^{- 2}$

Step 2

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

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

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

$b^{3} {(\frac{b}{3})}^{2}$

Step 4

Apply the product rule to $\frac{b}{3}$ .

$b^{3} \frac{b^{2}}{3^{2}}$

Step 5

Raise $3$ to the power of $2$ .

$b^{3} \frac{b^{2}}{9}$

Step 6

Multiply $b^{3} \frac{b^{2}}{9}$ .

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Step 6.1

Combine $b^{3}$ and $\frac{b^{2}}{9}$ .

$\frac{b^{3} b^{2}}{9}$

Step 6.2

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

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Step 6.2.1

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

$\frac{b^{3 + 2}}{9}$

Step 6.2.2

Add $3$ and $2$ .

$\frac{b^{5}}{9}$