Answer: [tex]r^{-3/4}[/tex]
*Accidentally turned f into r*
Step-by-step explanation:
Fractional exponents are actually quite simple :) I'll give a few examples and I'm sure you'll get it quick:
[tex]x^{1/2} = \sqrt[2]{x^1} \\x^{2/3}=\sqrt[3]{x^2} \\x^{71/984}=\sqrt[984]{x^{71}}[/tex]
As you can see, the numerator of the fraction becomes an exponent, and the denominator becomes a radical.
So to simplify this question first make [tex]({r^{1/3})^{-9/4}[/tex] into [tex]\sqrt[4]{ ({r}^{1/3})^{-9}}[/tex]An exponent raised to another exponent is the same as multiplying the exponents. Thus, we can multiply 1/3*-9.
[tex]\sqrt[4]{r^{-3}}[/tex]
Then we can use what we learned earlier to make it:
[tex]r^{-3/4}[/tex]
