properties of rational exponents HELP

fairiean9el · #1 Jan 22, 2005, 07:32 PM

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!!! =]

reinsuranc · Jan 26, 2005, 04:01 AM

( 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



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