Simplify ((-3j^2)/(a^-2k^2))^3

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

Step 1

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

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

Step 2

Move the negative in front of the fraction.

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

Step 3

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

Apply the product rule to $- \frac{3 j^{2} a^{2}}{k^{2}}$ .

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

Apply the product rule to $\frac{3 j^{2} a^{2}}{k^{2}}$ .

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

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

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

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

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

Step 4

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

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

Step 5

Simplify the numerator.

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

$- \frac{27 {(j^{2})}^{3} {(a^{2})}^{3}}{{(k^{2})}^{3}}$

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

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

$- \frac{27 j^{2 \cdot 3} {(a^{2})}^{3}}{{(k^{2})}^{3}}$

Multiply $2$ by $3$ .

$- \frac{27 j^{6} {(a^{2})}^{3}}{{(k^{2})}^{3}}$

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

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

$- \frac{27 j^{6} a^{2 \cdot 3}}{{(k^{2})}^{3}}$

Multiply $2$ by $3$ .

$- \frac{27 j^{6} a^{6}}{{(k^{2})}^{3}}$

Step 6

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

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

$- \frac{27 j^{6} a^{6}}{k^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$- \frac{27 j^{6} a^{6}}{k^{6}}$