SOLUTION: i have a question. i am asked to put in simplest form. (2/3)^-2(4/5)^-1. im not sure about the answer. i think its 7/2 is that correct. i would appreciate the help. thanks a bunch

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: i have a question. i am asked to put in simplest form. (2/3)^-2(4/5)^-1. im not sure about the answer. i think its 7/2 is that correct. i would appreciate the help. thanks a bunch      Log On


   

Question 276679: i have a question. i am asked to put in simplest form. (2/3)^-2(4/5)^-1. im not sure about the answer. i think its 7/2 is that correct. i would appreciate the help. thanks a bunch
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2F3%29%5E%28-2%29%284%2F5%29%5E%28-1%29
A -1 as an exponent means "reciprocal of" so %284%2F5%29%5E%28-1%29+=+5%2F4
A -2 as an exponent means "reciprocal of the square" (or "square of the reciprocal") so %282%2F3%29%5E%28-2%29+=+%283%2F2%29%5E2+=+9%2F4
Substituting these into your expression we get:
%289%2F4%29%285%2F4%29
which simplifies to
45%2F16
which, as a mixed number is
2%2613%2F16