Write the Fraction in Simplest Form (-6j^-9)/((-2j^4)^3)

$\frac{- 6 j^{- 9}}{{(- 2 j^{4})}^{3}}$

Move $j^{- 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 6}{{(- 2 j^{4})}^{3} j^{9}}$

Simplify the denominator.

Apply the product rule to $- 2 j^{4}$ .

$\frac{- 6}{{(- 2)}^{3} {(j^{4})}^{3} j^{9}}$

Raise $- 2$ to the power of $3$ .

$\frac{- 6}{- 8 {(j^{4})}^{3} j^{9}}$

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

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

$\frac{- 6}{- 8 j^{4 \cdot 3} j^{9}}$

Multiply $4$ by $3$ .

$\frac{- 6}{- 8 j^{12} j^{9}}$

Multiply $j^{12}$ by $j^{9}$ by adding the exponents.

Move $j^{9}$ .

$\frac{- 6}{- 8 (j^{9} j^{12})}$

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

$\frac{- 6}{- 8 j^{9 + 12}}$

Add $9$ and $12$ .

$\frac{- 6}{- 8 j^{21}}$

Cancel the common factor of $- 6$ and $- 8$ .

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

$\frac{- 2 (3)}{- 8 j^{21}}$

Cancel the common factors.

Factor $- 2$ out of $- 8 j^{21}$ .

$\frac{- 2 (3)}{- 2 (4 j^{21})}$

Cancel the common factor.

$\frac{- 2 \cdot 3}{- 2 (4 j^{21})}$

Rewrite the expression.

$\frac{3}{4 j^{21}}$