what is the answer to " 2^5/2 - 2^3/2 "

Question

This is a sample question from a college level math placement assessment. It seems so simple but yet i can not do i. I need help please. 

Answer 1

2^(5/2) - 2^(3/2)

 

 

When we have fractional exponents, we have radical terms.

 

Apply these rules:

 

x^{(m / n)} = ⁿ√(x^m)

 

x^{(n / n)} = ⁿ√(xⁿ) = x

 

 

√(2⁵) - √(2³)

 

 

Break down the radical terms by their factors.

 

√(2²) √(2²) √(2) - √(2²) √(2) =

 

 2 * 2 * √(2) - 2 * √(2) =

 

  4√2 - 2√2 =

 

    2√2

 

 

Putting this result in exponent form,

 

2 * 2^(1/2) =

 

2^(3/2)

Answer 2

Take advantage of the properties of rational exponents.

 

a^c/b = ^b√a^c = (^b√a)^c

 

In your case:

 

2^5/2 = √2⁵ = √32

 

2^3/2 = √2³ = √8

 

So you end up with 

 

√32 - √8 = 4√2 - 2√2 = 2√2

 

EDIT: In response to the comment.

 

Follow the same rules.

3^7/3 - 3^4/3
= ³√3⁷ - ³√3⁴
= ³√3³*³√3³*³√3*-³√3³*³√3
= 3*3*³√3 - 3*³√3
= 9*³√3 - 3*³√3
= 6³√3

Answer 3

Dear Nael,

     If you have a 3 in the denominator, instead of a 2, you have to write it with the radical with a 3 because it is a

 

cubic root.   Let's look at the example that you gave:

 

 

  3^(7/3) - 3 ^(4/3)   =   ³√(3^7)   -    ³√(3^(4) )  You want to break it up in such a way that it is easy to find the

 

cubic root.

 

                                      [³√3^(3)  *       ³√3^(3)     *    ³√ 3^(1) ]  -   [ ³√ 3^(3)   *    ³√3^(1)]

                                     

                                      

                                       3* 3* ³√3   - 3* ³√3=   9 * ³√ 3   -   3 ³√3=_________I'll let you simplify.

 

If I have helped you, please give me a thumbs up.

 

                                                                         Susan C.