SOLUTION: Quick question, I dont understand why 2^(5/2)-2^(3/2) simplified down will equal 2^(3/2). Heres my work and I'm looking for clarification on this part = 2^3/2*2^2/2 - 2^3/2. Why a

Algebra ->  Exponents -> SOLUTION: Quick question, I dont understand why 2^(5/2)-2^(3/2) simplified down will equal 2^(3/2). Heres my work and I'm looking for clarification on this part = 2^3/2*2^2/2 - 2^3/2. Why a      Log On


   

Question 759755: Quick question, I dont understand why 2^(5/2)-2^(3/2) simplified down will equal 2^(3/2).
Heres my work and I'm looking for clarification on this part = 2^3/2*2^2/2 - 2^3/2. Why are they multiplying?
2^5/2 - 2^3/2
=2^(3/2+2/2) - 2^3/2
= 2^3/2*2^2/2 - 2^3/2
=2^3/2(2-1)
= 2^3/2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
2%5E%285%2F2%29-2%5E%283%2F2%29

clarification on this part: 2%5E%283%2F2%29%2A2%5E%282%2F2%29+-+2%5E3%2F2
if you have 2%5E%285%2F2%29 you can write exponent %285%2F2%29 as %283%2F2%2B2%2F2%29, then you have 2%5E%285%2F2%29=2%5E%283%2F2%2B2%2F2%29, then you use multiplication rule and write +2%5E%283%2F2%2B2%2F2%29 as a product like this 2%5E%283%2F2%29%2A2%5E%282%2F2%29
now back to 2%5E%283%2F2%29%2A2%5E%282%2F2%29+-+2%5E%283%2F2%29...factor
2%5E%283%2F2%29%282%5E%282%2F2%29+-+1%29....write 2%5E%282%2F2%29 as sqrt%282%5E2%29 and you see that is equal 2
2%5E%283%2F2%29%282+-+1%29
2%5E%283%2F2%29%2A1
2%5E%283%2F2%29
sqrt%282%5E3%29
2sqrt%282%29......simple form
2%2A1.41
2.82...final result