SOLUTION: Simplify. Write with positive exponents. [(b^3/4)/(a^-1/2)]^8

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: Simplify. Write with positive exponents. [(b^3/4)/(a^-1/2)]^8      Log On


   

Question 817140: Simplify. Write with positive exponents.
[(b^3/4)/(a^-1/2)]^8
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28b%5E%283%2F4%29%2Fa%5E%28-1%2F2%29%29%5E8
To start we can use the %28a%2Fb%29%5En+=+a%5En%2Fb%5En rule to raise the fraction to the 8th power:
%28b%5E%283%2F4%29%29%5E8%2F%28a%5E%28-1%2F2%29%29%5E8
Next we use the %28a%5En%29%5Em+=+a%5E%28n%2Am%29 rule to raise the powers of a power:
b%5E%28%283%2F4%29%2A8%29%2Fa%5E%28%28-1%2F2%29%2A8%29
Simplifying...
b%5E6%2Fa%5E%28-4%29

Now we will deal with the negative exponent. (Some like to deal with this first. But I prefer to wait until the end. Sometimes the negative exponents disappear on their own while working out the rest of the problem. In those cases it would be been a waste of time to have bothered with them at the start.) Since a%5E%28-n%29+=+1%2Fa%5En our expression becomes:
b%5E6%2F%281%2Fa%5E4%29
which simplifies to:
a%5E4+%2A+b%5E6