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

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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)   (Show Source): You can put this solution on YOUR website!
We're going to use the following identities

1)


2)


3)


Start with the given expression.


Use identity # 1 to divide the variable terms.


Rewrite as


Multiply by to get


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


Combine like terms.


Reduce.


Now use identity # 3


Rewrite as


Use identity # 2 to multiply the exponents.


Multiply 3 and to get


Reduce.


Evaluate to get 16


Rewrite 27 as


Use identity # 2 to multiply the exponents.


Multiply 3 and to get


Reduce.


Raise 3 to the 4th power to get 81



So where every variable is positive.
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