Simplify ((3k^5)^-2)/(5s^-5k^-5)

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

Simplify the expression.

Move ${(3 k^{5})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{5 s^{- 5} k^{- 5} {(3 k^{5})}^{2}}$

Move $s^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Move $k^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{s^{5} k^{5}}{5 {(3 k^{5})}^{2}}$

Simplify the denominator.

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

$\frac{s^{5} k^{5}}{5 \cdot 3^{2} {(k^{5})}^{2}}$

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

$\frac{s^{5} k^{5}}{5 \cdot 9 {(k^{5})}^{2}}$

Multiply the exponents in ${(k^{5})}^{2}$ .

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

$\frac{s^{5} k^{5}}{5 \cdot 9 k^{5 \cdot 2}}$

Multiply $5$ by $2$ .

$\frac{s^{5} k^{5}}{5 \cdot 9 k^{10}}$

Multiply $5$ by $9$ .

$\frac{s^{5} k^{5}}{45 k^{10}}$

Cancel the common factor of $k^{5}$ and $k^{10}$ .

Factor $k^{5}$ out of $s^{5} k^{5}$ .

$\frac{k^{5} s^{5}}{45 k^{10}}$

Cancel the common factors.

Factor $k^{5}$ out of $45 k^{10}$ .

$\frac{k^{5} s^{5}}{k^{5} (45 k^{5})}$

Cancel the common factor.

$\frac{k^{5} s^{5}}{k^{5} (45 k^{5})}$

Rewrite the expression.

$\frac{s^{5}}{45 k^{5}}$