SOLUTION: Simplify: <pre> (27B^1/3C^3/4 ) ^4/3 (----------- -) ( 8B^-2/3C^1/2) </pre> Entire expression is in parenthesis with outer exponent 4/3

Algebra ->  Rational-functions -> SOLUTION: Simplify: <pre> (27B^1/3C^3/4 ) ^4/3 (----------- -) ( 8B^-2/3C^1/2) </pre> Entire expression is in parenthesis with outer exponent 4/3      Log On


   

Question 310502: Simplify: 

(27B^1/3C^3/4 ) ^4/3
(-------------)
( 8B^-2/3C^1/2)


Entire expression is in parenthesis with outer exponent 4/3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We're going to use the following identities

1) %28x%5E%28y%29%29%2F%28x%5E%28z%29%29=x%5E%28y-z%29


2) %28x%5E%28y%29%29%5Ez=x%5E%28y%2Az%29


3) %28a%2Fb%29%5Ex=%28a%5Ex%29%2F%28b%5Ex%29


Start with the given expression.


Use identity # 1 to divide the variable terms.


Rewrite 1%2F3-%28-2%2F3%29 as 1%2F3%2B2%2F3


Multiply 1%2F2 by 2%2F2 to get 2%2F4


Combine the fractions by combining the numerators over the common denominator.


%28%2827b%5E%283%2F3%29c%5E%281%2F4%29%5E%22%22%29%2F8%29%5E%284%2F3%29%5E%22%22 Combine like terms.


%28%2827b%5E1c%5E%281%2F4%29%5E%22%22%29%2F8%29%5E%284%2F3%29%5E%22%22 Reduce.


Now use identity # 3


Rewrite 8 as 2%5E3


Use identity # 2 to multiply the exponents.


Multiply 3 and 4%2F3 to get 12%2F3


%28%2827b%5E1c%5E%281%2F4%29%5E%22%22%29%5E%284%2F3%29%5E%22%22%29%2F%282%5E4%29 Reduce.


%28%2827b%5E1c%5E%281%2F4%29%5E%22%22%29%5E%284%2F3%29%5E%22%22%29%2F%2816%29 Evaluate 2%5E4 to get 16


%28%283%5E3b%5E1c%5E%281%2F4%29%5E%22%22%29%5E%284%2F3%29%5E%22%22%29%2F%2816%29 Rewrite 27 as 3%5E3


Use identity # 2 to multiply the exponents.


%283%5E%2812%2F3%29b%5E%284%2F3%29c%5E%284%2F12%29%5E%22%22%29%2F%2816%29 Multiply 3 and 4%2F3 to get 12%2F3


%283%5E4b%5E%284%2F3%29c%5E%281%2F3%29%5E%22%22%29%2F%2816%29 Reduce.


%2881b%5E%284%2F3%29c%5E%281%2F3%29%5E%22%22%29%2F%2816%29 Raise 3 to the 4th power to get 81



So where every variable is positive.