Simplify (3x^2)^-3

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

Step 1

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

$\frac{1}{{(3 x^{2})}^{3}}$

Step 2

Simplify the denominator.

Apply the product rule to $3 x^{2}$ .

$\frac{1}{3^{3} {(x^{2})}^{3}}$

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

$\frac{1}{27 {(x^{2})}^{3}}$

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

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

$\frac{1}{27 x^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\frac{1}{27 x^{6}}$