SOLUTION: Provide the class with a third expression to simplify that includes rational (fractional) exponents.

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Question 126529: Provide the class with a third expression to
simplify that includes rational (fractional) exponents.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say you had the expression


%28x%5E%281%2F2%29%2Ax%5E%283%2F2%29%29%2Fx%5E%283%2F4%29 (note: the top two exponents from left to right are 1%2F2 and 3%2F2



Now let's simplify:



%28x%5E%281%2F2%29%2Ax%5E%283%2F2%29%29%2Fx%5E%283%2F4%29 Start with the given expression


%28x%5E%281%2F2%2B3%2F2%29%29%2Fx%5E%283%2F4%29 Multiply the numerators by adding the exponents


%28x%5E2%29%2Fx%5E%283%2F4%29 Add the exponents 1%2F2 and 3%2F2 to get 1%2F2%2B3%2F2=%281%2B3%29%2F2=4%2F2=2


x%5E%282-3%2F4%29 Divide the expression by subtracting the exponents


x%5E%285%2F4%29 Subtract the exponents 3%2F4 from 2 to get 2-3%2F4=8%2F4-3%2F4=%288-3%29%2F4=5%2F4



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Answer:

So %28x%5E%281%2F2%29%2Ax%5E%283%2F2%29%29%2Fx%5E%283%2F4%29 simplifies to x%5E%285%2F4%29 (this says x to the fraction power 5%2F4)



In other words, %28x%5E%281%2F2%29%2Ax%5E%283%2F2%29%29%2Fx%5E%283%2F4%29=x%5E%285%2F4%29