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

`x^{(1)/(2) } + 48`

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^{(2)/(4)} = x^{(1)/(2) }`

Combine them using addition, since addition was in the problem

`x^{(1)/(2) } + 48`

I hope this helps!