How do you simplify without a fractional exponent?

Question

1.) 12^3/2

2.) (-8)^5/3

     -----------

     (-8)^4/3

 

 

Answer 1

1) 12^(3/2)=√12³=√12x12x12=√12x12x2x2x3=12x2√3=24√3

 

2)(-8)^(5/3)=[(-2)³]^(5/3)=(-2)^(3)(5/3)=(-2)⁵=-32

 

(-8)^(4/3)=[(-2)³]^(4/3)=(-2)⁴=16

Answer 2

1. 12^3/2 = (12³)^1/2 = (12²*12)^1/2 = 12(4*3)^1/2 = 24(3)^1/2 = 24√3
2. (-8)^5/3 = (-2³)^5/3 = -2⁵ = -32
3. (-8)^4/3 = (-2³)^4/3 = (-2)⁴ = 16

 

But if you meant (-8)^5/3/(-8)^4/3:

 

(-8)^5/3/(-8)^4/3

 

= (-8)^5/3-4/3    [Exponent Property:  x^a/x^b = x^a-b)

 

= (-8)^1/3

 

= (-2³)^1/3

 

= -2