Simplify (6j^-2)^-3

${(6 j^{- 2})}^{- 3}$

Step 1

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

${(6 \frac{1}{j^{2}})}^{- 3}$

Step 2

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

${(\frac{6}{j^{2}})}^{- 3}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{j^{2}}{6})}^{3}$

Step 4

Apply the product rule to $\frac{j^{2}}{6}$ .

$\frac{{(j^{2})}^{3}}{6^{3}}$

Step 5

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

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

$\frac{j^{2 \cdot 3}}{6^{3}}$

Multiply $2$ by $3$ .

$\frac{j^{6}}{6^{3}}$

Step 6

Raise $6$ to the power of $3$ .

$\frac{j^{6}}{216}$