Write the Fraction in Simplest Form (-3(j^-3a^4)^-3)/(3j^4a^8)

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

Step 1

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

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

Step 2

Cancel the common factor of $- 3$ and $3$ .

Factor $3$ out of $- 3$ .

$\frac{3 \cdot - 1}{3 j^{4} a^{8} {(j^{- 3} a^{4})}^{3}}$

Cancel the common factors.

Factor $3$ out of $3 j^{4} a^{8} {(j^{- 3} a^{4})}^{3}$ .

$\frac{3 \cdot - 1}{3 (j^{4} a^{8} {(j^{- 3} a^{4})}^{3})}$

Cancel the common factor.

$\frac{3 \cdot - 1}{3 (j^{4} a^{8} {(j^{- 3} a^{4})}^{3})}$

Rewrite the expression.

$\frac{- 1}{j^{4} a^{8} {(j^{- 3} a^{4})}^{3}}$

Step 3

Simplify the denominator.

Apply the product rule to $j^{- 3} a^{4}$ .

$\frac{- 1}{j^{4} a^{8} {(j^{- 3})}^{3} {(a^{4})}^{3}}$

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

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

$\frac{- 1}{j^{4} a^{8} j^{- 3 \cdot 3} {(a^{4})}^{3}}$

Multiply $- 3$ by $3$ .

$\frac{- 1}{j^{4} a^{8} j^{- 9} {(a^{4})}^{3}}$

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

$\frac{- 1}{j^{4} a^{8} \frac{1}{j^{9}} {(a^{4})}^{3}}$

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

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

$\frac{- 1}{j^{4} a^{8} \frac{1}{j^{9}} a^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$\frac{- 1}{j^{4} a^{8} \frac{1}{j^{9}} a^{12}}$

Combine exponents.

Combine $j^{4}$ and $\frac{1}{j^{9}}$ .

$\frac{- 1}{a^{8} \frac{j^{4}}{j^{9}} a^{12}}$

Combine $a^{8}$ and $\frac{j^{4}}{j^{9}}$ .

$\frac{- 1}{\frac{a^{8} j^{4}}{j^{9}} a^{12}}$

Combine $\frac{a^{8} j^{4}}{j^{9}}$ and $a^{12}$ .

$\frac{- 1}{\frac{a^{8} j^{4} a^{12}}{j^{9}}}$

Multiply $a^{8}$ by $a^{12}$ by adding the exponents.

Move $a^{12}$ .

$\frac{- 1}{\frac{a^{12} a^{8} j^{4}}{j^{9}}}$

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

$\frac{- 1}{\frac{a^{12 + 8} j^{4}}{j^{9}}}$

Add $12$ and $8$ .

$\frac{- 1}{\frac{a^{20} j^{4}}{j^{9}}}$

Reduce the expression $\frac{a^{20} j^{4}}{j^{9}}$ by cancelling the common factors.

Factor $j^{4}$ out of $a^{20} j^{4}$ .

$\frac{- 1}{\frac{j^{4} a^{20}}{j^{9}}}$

Factor $j^{4}$ out of $j^{9}$ .

$\frac{- 1}{\frac{j^{4} a^{20}}{j^{4} j^{5}}}$

Cancel the common factor.

$\frac{- 1}{\frac{j^{4} a^{20}}{j^{4} j^{5}}}$

Rewrite the expression.

$\frac{- 1}{\frac{a^{20}}{j^{5}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$- \frac{j^{5}}{a^{20}}$

Write the Fraction in Simplest Form (-3(j^-3a^4)^-3)/(3j^4a^8)

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