Simplify (-3x^-2)^3

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

Step 1

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

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

Step 2

Combine $- 3$ and $\frac{1}{x^{2}}$ .

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

Step 3

Move the negative in front of the fraction.

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

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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

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

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

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

Step 5

Raise $- 1$ to the power of $3$ .

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

Step 6

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

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

Step 7

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

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

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

Multiply $2$ by $3$ .

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