Simplify (3a^-2b^-2)/(18b^3)

$\frac{3 a^{- 2} b^{- 2}}{18 b^{3}}$

Step 1

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

$\frac{3 b^{- 2}}{18 b^{3} a^{2}}$

Step 2

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

$\frac{3}{18 b^{3} a^{2} b^{2}}$

Step 3

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

Move $b^{2}$ .

$\frac{3}{18 (b^{2} b^{3}) a^{2}}$

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

$\frac{3}{18 b^{2 + 3} a^{2}}$

Add $2$ and $3$ .

$\frac{3}{18 b^{5} a^{2}}$

Step 4

Cancel the common factor of $3$ and $18$ .

Factor $3$ out of $3$ .

$\frac{3 (1)}{18 b^{5} a^{2}}$

Cancel the common factors.

Factor $3$ out of $18 b^{5} a^{2}$ .

$\frac{3 (1)}{3 (6 b^{5} a^{2})}$

Cancel the common factor.

$\frac{3 \cdot 1}{3 (6 b^{5} a^{2})}$

Rewrite the expression.

$\frac{1}{6 b^{5} a^{2}}$