Simplify simplify (3s^8)^-5

simplify ${(3 s^{8})}^{- 5}$

Step 1

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

$\frac{1}{{(3 s^{8})}^{5}}$

Step 2

Simplify the denominator.

Apply the product rule to $3 s^{8}$ .

$\frac{1}{3^{5} {(s^{8})}^{5}}$

Raise $3$ to the power of $5$ .

$\frac{1}{243 {(s^{8})}^{5}}$

Multiply the exponents in ${(s^{8})}^{5}$ .

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

$\frac{1}{243 s^{8 \cdot 5}}$

Multiply $8$ by $5$ .

$\frac{1}{243 s^{40}}$