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

Question

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

y 6/7

____________

y 3/7

Answer 1

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 y^3/7

 

Answer 2

You can also look at the problem as follows:

     y^6/7 / y^3/7 = 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 = y^3/7 

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 / x^5/6