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

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

Tutors, please sign in to answer this question.

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}

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}

Dana R.

English/Math SAT PrepTutor with PhD

Lynbrook, NY

4.8
(85 ratings)

Timothy R.

Top Mathematics and Physics Tutor | Flexible

Avenel, NJ

4.8
(134 ratings)

Romina A.

Knowledgeable tutor in Spanish, Biology, Anatomy & Physiology and Math

Harrison, NJ

5.0
(169 ratings)

## Comments

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.