Sure, let's simplify the given expression step-by-step:
Given expression: [tex]\(\frac{r^{-4}}{3 s^5}\)[/tex]
Step 1: Recall the rule for negative exponents. A negative exponent [tex]\(\frac{1}{a^n}\)[/tex] can be rewritten as [tex]\(a^{-n} = 1/a^n\)[/tex]. Therefore, [tex]\(r^{-4}\)[/tex] can be rewritten as [tex]\(\frac{1}{r^4}\)[/tex].
Step 2: Substitute this into the expression:
[tex]\[
\frac{\frac{1}{r^4}}{3 s^5}
\][/tex]
Step 3: Simplify the fraction inside the fraction:
[tex]\[
= \frac{1}{3 r^4 s^5}
\][/tex]
So the simplified expression is:
[tex]\[
\frac{1}{3 r^4 s^5}
\][/tex]
Thus, the final result is:
[tex]\[
\frac{1}{3 r^4 s^5}
\][/tex]
