SOLUTION: Hi! I see a problem worked liked this: 8^2/3 = 8^1/3 * 8^1/3 = (8^1/3)^2 = 2^2 = 4 I don't understand how to they get from 8^2/3 to 8^1/3 * 8^1/3, from 8^1/3 * 8^1/3 to (8^1/3)^2

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: Hi! I see a problem worked liked this: 8^2/3 = 8^1/3 * 8^1/3 = (8^1/3)^2 = 2^2 = 4 I don't understand how to they get from 8^2/3 to 8^1/3 * 8^1/3, from 8^1/3 * 8^1/3 to (8^1/3)^2      Log On


   

Question 263081: Hi! I see a problem worked liked this:
8^2/3 = 8^1/3 * 8^1/3 = (8^1/3)^2 = 2^2 = 4
I don't understand how to they get from 8^2/3 to 8^1/3 * 8^1/3, from 8^1/3 * 8^1/3 to (8^1/3)^2, and from (8^1/3)^2 to 2^2. I put it this way because I don't understand how the process works of each step.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Recall that a%5E%28b%2Bc%29=a%5Eb%2Aa%5Ec. Because 2%2F3=%281%2B1%29%2F3=1%2F3%2B1%2F3, we can say that 8%5E%282%2F3%29=8%5E%281%2F3%29%2A8%5E%281%2F3%29%5E%22%22 using the identity a%5E%28b%2Bc%29=a%5Eb%2Aa%5Ec


Remember that exponentiation is just a way of repeated multiplication. When I say 2*2*2*2 I also mean 2%5E4. If I want to multiply 10 twos together, then I can say 2%5E10 and it saves me from writing out 10 twos. Because we have two 8%5E%281%2F3%29%5E%22%22 terms, we can write 8%5E%282%2F3%29=8%5E%281%2F3%29%2A8%5E%281%2F3%29=%288%5E%281%2F3%29%29%5E2


Now convert to radical notation to go from 8%5E%281%2F3%29%5E%22%22 to root%283%2C8%29. So %288%5E%281%2F3%29%29%5E2=%28root%283%2C8%29%29%5E2


Now take the cube root of 8 to get 2. This means that

%28root%283%2C8%29%29%5E2=2%5E2