Simplify (2a^-2)(3a^3b^2)(c^-2)

$(2 a^{- 2}) (3 a^{3} b^{2}) (c^{- 2})$

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

Move $a^{3}$ .

$2 (a^{3} a^{- 2}) (3 b^{2}) c^{- 2}$

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

$2 a^{3 - 2} (3 b^{2}) c^{- 2}$

Subtract $2$ from $3$ .

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

Simplify $2 a^{1} (3 b^{2}) c^{- 2}$ .

$2 a (3 b^{2}) c^{- 2}$

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $3$ .

$6 a b^{2} c^{- 2}$

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

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

Multiply $6 a b^{2} \frac{1}{c^{2}}$ .

Combine $6$ and $\frac{1}{c^{2}}$ .

$a b^{2} \frac{6}{c^{2}}$

Combine $a$ and $\frac{6}{c^{2}}$ .

$b^{2} \frac{a \cdot 6}{c^{2}}$

Combine $b^{2}$ and $\frac{a \cdot 6}{c^{2}}$ .

$\frac{b^{2} (a \cdot 6)}{c^{2}}$

Move $6$ to the left of $b^{2} a$ .

$\frac{6 b^{2} a}{c^{2}}$