Algebra Examples

$\frac{- 6 j^{- 8}}{- 2 {(j^{- 3})}^{5}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Move $j^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 6}{- 2 {(j^{- 3})}^{5} j^{8}}$

Step 1.2

Cancel the common factor of $- 6$ and $- 2$ .

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Step 1.2.1

Factor $- 2$ out of $- 6$ .

$\frac{- 2 (3)}{- 2 {(j^{- 3})}^{5} j^{8}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $- 2$ out of $- 2 {(j^{- 3})}^{5} j^{8}$ .

$\frac{- 2 (3)}{- 2 ({(j^{- 3})}^{5} j^{8})}$

Step 1.2.2.2

Cancel the common factor.

$\frac{- 2 \cdot 3}{- 2 ({(j^{- 3})}^{5} j^{8})}$

Step 1.2.2.3

Rewrite the expression.

$\frac{3}{{(j^{- 3})}^{5} j^{8}}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply the exponents in ${(j^{- 3})}^{5}$ .

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Step 2.1.1

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

$\frac{3}{j^{- 3 \cdot 5} j^{8}}$

Step 2.1.2

Multiply $- 3$ by $5$ .

$\frac{3}{j^{- 15} j^{8}}$

Step 2.2

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

$\frac{3}{\frac{1}{j^{15}} j^{8}}$

Step 3

Simplify terms.

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Step 3.1

Combine $\frac{1}{j^{15}}$ and $j^{8}$ .

$\frac{3}{\frac{j^{8}}{j^{15}}}$

Step 3.2

Reduce the expression $\frac{j^{8}}{j^{15}}$ by cancelling the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{3}{\frac{j^{8} \cdot 1}{j^{15}}}$

Step 3.2.2

Factor $j^{8}$ out of $j^{15}$ .

$\frac{3}{\frac{j^{8} \cdot 1}{j^{8} j^{7}}}$

Step 3.2.3

Cancel the common factor.

$\frac{3}{\frac{j^{8} \cdot 1}{j^{8} j^{7}}}$

Step 3.2.4

Rewrite the expression.

$\frac{3}{\frac{1}{j^{7}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$3 j^{7}$