Write the Fraction in Simplest Form ((3s^5)^-4)/(6s^3j^-6)

$\frac{{(3 s^{5})}^{- 4}}{6 s^{3} j^{- 6}}$

Step 1

Move ${(3 s^{5})}^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{6 s^{3} j^{- 6} {(3 s^{5})}^{4}}$

Step 2

Move $j^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{j^{6}}{6 s^{3} {(3 s^{5})}^{4}}$

Step 3

Simplify the denominator.

Apply the product rule to $3 s^{5}$ .

$\frac{j^{6}}{6 s^{3} \cdot 3^{4} {(s^{5})}^{4}}$

Raise $3$ to the power of $4$ .

$\frac{j^{6}}{6 s^{3} \cdot 81 {(s^{5})}^{4}}$

Multiply the exponents in ${(s^{5})}^{4}$ .

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

$\frac{j^{6}}{6 s^{3} \cdot 81 s^{5 \cdot 4}}$

Multiply $5$ by $4$ .

$\frac{j^{6}}{6 s^{3} \cdot 81 s^{20}}$

Combine exponents.

Multiply $81$ by $6$ .

$\frac{j^{6}}{486 s^{3} s^{20}}$

Multiply $s^{3}$ by $s^{20}$ by adding the exponents.

Move $s^{20}$ .

$\frac{j^{6}}{486 (s^{20} s^{3})}$

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

$\frac{j^{6}}{486 s^{20 + 3}}$

Add $20$ and $3$ .

$\frac{j^{6}}{486 s^{23}}$