Simplify b^3(3b^-1)^-2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Add $3$ and $2$ .

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