Me with this question! i'm so confused.

which is equivalent to square root of 5?

a) 5^2
b) 5^(-2)
c) 5^1/2
d) 5^(-1/2)

show your wok.

The answer is:  [C]:  "  5^(1/2) " .

Explanation:

The square root of 5 is expressed as:

     √5 .

Note: The cubic root of 5 would be expressed as:

         ∛5 .

So, the "square root of 5" is actually:

        ²√5  .   By convention, for "square roots", we eliminate 
                      "superscript 2".

Also, note that:  √5 = ²√5 = ²√(5¹) ; 

Since "5¹ = 5" ; 

    By convention we often eliminate the "{raised to the power of 1}" .

So, √5 = ²√5 = ²√(5¹) = 5^(1/2) ; 

Thus,  √5 = 5^(1/2) ; 

In the "(1/2)" power, the "1" comes from the [implied exponent]
                                 of "1" in " 5¹ " ; and the "2" comes from the "square
                                                                                                        root". 

Note that  "5^(3/2) = ²√(5³) = √(5³)   = √(5*5*5) = √5* √5 *√5 = 5√5 .

Note that "6^(4/3) = ∛ (6⁴).

A bit too lengthy, but hope this explanation helps.