I need help!!

[Beethequeen]

Hey guys! I am needing help on a few problems tonight..

Can you explain how to write as a simple fraction WITHOUT using a calculator?

1) 16 to the 3/4 the power

2) (1/5) to the -1/4 power

3) 36 to the -1/2 power


THANK YOU!!

 

[soroban]

Hello, Beethequeen!

\(\displaystyle 1)\;16^{\frac{3}{4}}\)

\(\displaystyle 16^{\frac{3}{4}} \;=\;\left(\sqrt[4]{16}\right)^3 \;=\;(2)^3 \;=\;8\)

\(\displaystyle 2)\;\left(\dfrac{1}{5}\right)^{-\frac{1}{4}}\)

\(\displaystyle \left(\dfrac{1}{5}\right)^{-\frac{1}{4}} \;=\;\left(\dfrac{5}{1}\right)^{\frac{1}{4}} \;=\;\sqrt[4]{5} \)

\(\displaystyle 3)\;36^{-\frac{1}{2}}\)

\(\displaystyle 36^{-\frac{1}{2}} \;=\;\dfrac{1}{36^{\frac{1}{2}}} \;=\;\dfrac{1}{\sqrt{36}} \;=\;\dfrac{1}{6}\)

 

[Beethequeen]

Thank you!!
I have a question..the answer to (1/5) to the power of -1/4 is not in fraction form. However, is this still the answer to writing it as a simple fraction??