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I am working with rational exponents. I have to answer with positive exponents. y 6/7 over y 3/7.

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2 Answers

Hi, Kristine.

Since you have the same base y in both the numerator and denominator, you can subtract the exponents to simplify the expression.

6/7 - 3/7 = 3/7 so your answer is y3/7



Thanks, for this let me see if I got it right. X -5/6 would be the reciprocal to make it positive 1 over X 5/6.

You can also look at the problem as follows:

     y6/7 / y3/7 = y(1/7)·6 / y(1/7)·3 = (y(1/7))6 / (y(1/7))3 

Since the contents inside the parentheses are the same, subtract the smaller exponent (in this case, 3) from the exponent of the numerator and the denominator to simplify:

     (y(1/7))6-3 / (y(1/7))3-3 = (y(1/7))3 / (y(1/7))0 = (y(1/7))3 / 1 = (y(1/7))3 = y(1/7)·3 = y3/7 

As for when you have a negative exponent, you make it positive by finding the reciprocal of the expression.

And so,      x-(5/6)   ==>   x-(5/6) / 1   ==>   1 / x5/6