Question

Show all work to write the expression in simplified rational exponent form:
$(\sqrt[4]{x^{2}+4 } )^{3}$
(Fourth root of x squared plus four, cubed)

Answer 1

Answer:

$x^{\frac{1}{2} } + 48$

Step-by-step explanation:

This is hard to explain, but basically you use exponent rules to switch it to an exponent

$(\sqrt[4]{x^{2} +4} )^{3}$

It's easiest if you calculate $4^{3}$ first

4³ = 4 x 4 x 4 = 48

Then convert the root to a fraction exponent

$\sqrt[4]{x^{2}} = x^{\frac{2}{4}} = x^{\frac{1}{2} }$

Combine them using addition, since addition was in the problem

$x^{\frac{1}{2} } + 48$

I hope this helps!