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
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}
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.
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