SOLUTION: Simplify the expression: (1/8)^-2/3 + (1/4)^-1/2 I don't know how to do this! Do I find the LCD first? (1/8)^-2/3 + (2/8)^1/2

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Simplify the expression: (1/8)^-2/3 + (1/4)^-1/2 I don't know how to do this! Do I find the LCD first? (1/8)^-2/3 + (2/8)^1/2      Log On


   

Question 107732: Simplify the expression:
(1/8)^-2/3 + (1/4)^-1/2
I don't know how to do this! Do I find the LCD first?
(1/8)^-2/3 + (2/8)^1/2
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
You won't need an LCD for this one.

The first thing you need is a couple of rules:
1) a%5E%28-n%29=1%2Fa%5En

2) when you have an exponent of the form m%2Fn, it means to take the nth root of the expression raised to the m power.

%281%2F8%29%5E%28-2%2F3%29%2B%281%2F4%29%5E%28-1%2F2%29 is the original problem, so apply rule 1).

%281%2F%281%2F8%29%5E%282%2F3%29%29%2B%281%2F%281%2F4%29%5E%281%2F2%29%29

Now apply rule 2) to each of the terms:
The cube root of 8 is 2 and 2 squared is 4, and the square root of 4 is 2, so we can write:

%281%2F%281%2F4%29%29%2B%281%2F%281%2F2%29%29=4%2B2=6