How would I simplify 25^(3/2), leaving it as a fraction, not a whole number?

Question

Essentially the goal is to simplify 25^(3/2), and leave the answer as a fraction. I always end up with a whole number. Any assistance regarding this would be greatly appreciated, thanks in advance!

Answer 1

There are infinitely many ways to write an integer as a fraction (i.e. a ratio of two integers)...is this really what the question is asking?

 

In any case, 25^(3/2) can be simplified using exponent rules...25^(3/2)=25^(3*(1/2))=(25^3)^(1/2)=sqrt(15625)=125

 

or, alternatively, and simpler: 25^(3/2)=25^((1/2)*3)=(sqrt(25))^3=5^3=125

Answer 2

Hi Kyle,

 

  25^(3/2) = 5^3

                = 125

                = 250/2

or            

                = 500/4

 

or             =375/3

 

 

 

 

 

 

 

Meena from Strongsville,Oh