Simplify (-3^-2b^2)/(a^0b^-3)

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

Step 1

Move $3^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 1 b^{2}}{a^{0} b^{- 3} \cdot 3^{2}}$

Step 2

Move $b^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 3

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

Move $b^{3}$ .

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

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

$\frac{- 1 b^{3 + 2}}{3^{2}}$

Add $3$ and $2$ .

$\frac{- 1 b^{5}}{3^{2}}$

Step 4

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

$\frac{- 1 b^{5}}{9}$

Step 5

Move the negative in front of the fraction.

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