Question

I need to know the answer quick because I have to go somewhere

Answer 1

First, we need to remember to rules when working with exponents:

`\begin{gathered} (1)/(b^a)=b^(-a) \\ \text{and} \\ b^a\cdot b^c=b^(a+c) \end{gathered}`

So, going back to our problem

`\begin{gathered} \frac{2^{(3)/(4)}}{2^{(1)/(2)}} \\ =2^{(3)/(4)}\cdot2^{-(1)/(2)}=2^{(3)/(4)-(1)/(2)}=2^{(1)/(4)} \end{gathered}`

And this last result is equal to

`\begin{gathered} 2^{(1)/(4)}=\sqrt[4]{2} \\ \Rightarrow\frac{2^{(3)/(4)}}{2^{(1)/(2)}}=\sqrt[4]{2} \end{gathered}`