Algebra Examples

$\frac{{(j^{- 1} k^{3})}^{- 4}}{j^{3} k^{3}}$

Step 1

Move ${(j^{- 1} k^{3})}^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{j^{3} k^{3} {(j^{- 1} k^{3})}^{4}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $j^{- 1} k^{3}$ .

$\frac{1}{j^{3} k^{3} {(j^{- 1})}^{4} {(k^{3})}^{4}}$

Step 2.2

Multiply the exponents in ${(j^{- 1})}^{4}$ .

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Step 2.2.1

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

$\frac{1}{j^{3} k^{3} j^{- 1 \cdot 4} {(k^{3})}^{4}}$

Step 2.2.2

Multiply $- 1$ by $4$ .

$\frac{1}{j^{3} k^{3} j^{- 4} {(k^{3})}^{4}}$

Step 2.3

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

$\frac{1}{j^{3} k^{3} \frac{1}{j^{4}} {(k^{3})}^{4}}$

Step 2.4

Multiply the exponents in ${(k^{3})}^{4}$ .

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Step 2.4.1

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

$\frac{1}{j^{3} k^{3} \frac{1}{j^{4}} k^{3 \cdot 4}}$

Step 2.4.2

Multiply $3$ by $4$ .

$\frac{1}{j^{3} k^{3} \frac{1}{j^{4}} k^{12}}$

Step 2.5

Combine exponents.

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Step 2.5.1

Combine $j^{3}$ and $\frac{1}{j^{4}}$ .

$\frac{1}{k^{3} \frac{j^{3}}{j^{4}} k^{12}}$

Step 2.5.2

Combine $k^{3}$ and $\frac{j^{3}}{j^{4}}$ .

$\frac{1}{\frac{k^{3} j^{3}}{j^{4}} k^{12}}$

Step 2.5.3

Combine $\frac{k^{3} j^{3}}{j^{4}}$ and $k^{12}$ .

$\frac{1}{\frac{k^{3} j^{3} k^{12}}{j^{4}}}$

Step 2.5.4

Multiply $k^{3}$ by $k^{12}$ by adding the exponents.

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Step 2.5.4.1

Move $k^{12}$ .

$\frac{1}{\frac{k^{12} k^{3} j^{3}}{j^{4}}}$

Step 2.5.4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{\frac{k^{12 + 3} j^{3}}{j^{4}}}$

Step 2.5.4.3

Add $12$ and $3$ .

$\frac{1}{\frac{k^{15} j^{3}}{j^{4}}}$

Step 2.6

Reduce the expression $\frac{k^{15} j^{3}}{j^{4}}$ by cancelling the common factors.

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Step 2.6.1

Factor $j^{3}$ out of $k^{15} j^{3}$ .

$\frac{1}{\frac{j^{3} k^{15}}{j^{4}}}$

Step 2.6.2

Factor $j^{3}$ out of $j^{4}$ .

$\frac{1}{\frac{j^{3} k^{15}}{j^{3} j}}$

Step 2.6.3

Cancel the common factor.

$\frac{1}{\frac{j^{3} k^{15}}{j^{3} j}}$

Step 2.6.4

Rewrite the expression.

$\frac{1}{\frac{k^{15}}{j}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{j}{k^{15}}$

Step 4

Multiply $\frac{j}{k^{15}}$ by $1$ .

$\frac{j}{k^{15}}$