properties of rational exponents HELP
Hi ! I want to know if I answered this math problem correctly: the directions are to simplify the expression and assume all variables are positive.
Problem:
( 2 ^1/3 x 5 ^ 1/2 ) 4
My work:
( 2 ^1/3 x 5 ^ 1/2 ) 4 =
2 ^ 4/3 x 5 ^ 2 =
2 ^ 4/3 x 25
Thanks so much for helping!! =] :D
I don't think you are treating that 4 correctly
( 2 ^1/3 x 5 ^ 1/2 ) 4
I would like to rewrite and add some extra parentheses just to be clear:
( 2^(1/3) x 5^(1/2) ) x 4
( 2^(1/3) x 5^(1/2) x 2^2 )
( 2^(1/3) x 2^2 x 5^(1/2) )
( 2^(1/3 + 2) x 5^(1/2) ) ; this is because (y^a)times(y^b) = y^(a+b).
( 2^(7/3) x 5^(1/2) )
This equals about 11.27