Algebra Examples

$\frac{10 j^{- 3}}{- 2 {(j^{- 3})}^{3}}$

Step 1

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

$\frac{10}{- 2 {(j^{- 3})}^{3} j^{3}}$

Step 2

Cancel the common factor of $10$ and $- 2$ .

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Step 2.1

Factor $2$ out of $10$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Simplify the denominator.

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

Multiply $- 3$ by $3$ .

$\frac{5}{- j^{- 9} j^{3}}$

Step 3.2

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

$\frac{5}{- \frac{1}{j^{9}} j^{3}}$

Step 3.3

Combine $j^{3}$ and $\frac{1}{j^{9}}$ .

$\frac{5}{- \frac{j^{3}}{j^{9}}}$

Step 3.4

Reduce the expression $\frac{j^{3}}{j^{9}}$ by cancelling the common factors.

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Step 3.4.1

Multiply by $1$ .

$\frac{5}{- \frac{j^{3} \cdot 1}{j^{9}}}$

Step 3.4.2

Factor $j^{3}$ out of $j^{9}$ .

$\frac{5}{- \frac{j^{3} \cdot 1}{j^{3} j^{6}}}$

Step 3.4.3

Cancel the common factor.

$\frac{5}{- \frac{j^{3} \cdot 1}{j^{3} j^{6}}}$

Step 3.4.4

Rewrite the expression.

$\frac{5}{- \frac{1}{j^{6}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$5 (- j^{6})$

Step 5

Multiply $- 1$ by $5$ .

$- 5 j^{6}$