Question

PLEASE HELP I NEED THIS DONE!

What is the radical form of each of the given expressions?

Drag the answer into the box to match each expression.


5 2/3 -------- ???

5 1/2 -------- ???

3 2/5 -------- ???

3 5/2 ------- ???


Options:

√5 || √3^5 || ^5√3^2 || ^3√5^2 || √3 || ^3√5

Answer 1

Use the rule that says
`x^(y/z) = {}^z√(x^y)` to get the following:


`5^(2/3) = {}^3√(5^2)`


`5^(1/2) = {}^2√(5^1) = √(5)`


`3^(2/5) = {}^5√(3^2)`


`3^(5/2) = {}^2√(3^5) = √(3^5)`

Answer 2

Given an algebraic expression involving exponents

so, we can write it in radical form based on the fact that is
`x^{(a)/(n)}` equivalent to the nth root of
`x^a`

i.e,
`x^{(a)/(n)} =\sqrt[n]{x^a}`

Also, Use the following rule of exponents :
`(x^a)^b = x^(ab)`

then:

1.
`5^{(2)/(3)}` =
`(5^2)^{(1)/(3) }`=
`\sqrt[3]{5^2}`

2.
`5^{(1)/(2) }` =
`√(5)`

3.
`3^{(2)/(5)} = (3^2)^{(1)/(5) } = \sqrt[5]{3^2}`

4.
`3^{(5)/(2)} = (3^5)^{(1)/(2)} =√(3^5)`