Algebra Examples

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

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.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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.

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Step 5.1

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

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

Step 5.2

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

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Step 5.2.1

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

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

Step 5.2.2

Multiply $2$ by $3$ .

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

Step 5.3

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

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Step 5.3.1

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

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

Step 5.3.2

Multiply $2$ by $3$ .

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Multiply $2$ by $3$ .

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