Evaluate (3^-2a^-1)/(9^-1b^-2c^0)

$\frac{3^{- 2} a^{- 1}}{9^{- 1} b^{- 2} c^{0}}$

Step 1

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

$\frac{a^{- 1}}{9^{- 1} b^{- 2} c^{0} \cdot 3^{2}}$

Step 2

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

$\frac{1}{9^{- 1} b^{- 2} c^{0} \cdot 3^{2} a}$

Step 3

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

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

Multiply the exponents in ${(3^{2})}^{- 1}$ .

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

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

Multiply $2$ by $- 1$ .

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

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

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

Subtract $2$ from $2$ .

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

Step 4

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

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