Express 3^(3/2) in radical form

We have to express 3^(3/2) in radical form

Solution

We know that √x is expressed as x^1/2

Similarly we also know the exponential formula

a^m + an = a^m+n

So, 3^(3/2) = 3 1 + 3^1/2

3^(3/2) = 3 √3

Then to express in radical form, we must take the square of the number in front of the radical (as this is the inverse operation of taking the square root of something), and placing it under the root sign:

3^(3/2) = 3 √3 = √3 ³ = √27

Answer

3^(3/2) = 3 √3 = √3 ³ = √27