Write the Fraction in Simplest Form (10j^-3)/(-2(j^-3)^3)

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

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

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

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

Factor $2$ out of $10$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the denominator.

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

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

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

Multiply $- 3$ by $3$ .

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

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

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

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

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

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

Multiply by $1$ .

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply the numerator by the reciprocal of the denominator.

$5 (- j^{6})$

Multiply $- 1$ by $5$ .

$- 5 j^{6}$