Simplify (2(3x)^2)/((3x)^-2)

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

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

$2 {(3 x)}^{2} {(3 x)}^{2}$

Multiply ${(3 x)}^{2}$ by ${(3 x)}^{2}$ by adding the exponents.

Move ${(3 x)}^{2}$ .

$2 ({(3 x)}^{2} {(3 x)}^{2})$

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

$2 {(3 x)}^{2 + 2}$

Add $2$ and $2$ .

$2 {(3 x)}^{4}$

Apply the product rule to $3 x$ .

$2 (3^{4} x^{4})$

Raise $3$ to the power of $4$ .

$2 (81 x^{4})$

Multiply $81$ by $2$ .

$162 x^{4}$