SOLUTION: (3x+1)^1/2=4 how do you work a fraction as an exponent?

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Question 307374: (3x+1)^1/2=4 how do you work a fraction as an exponent?

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Raising to the 1/2 power means the same as "square root." In this equation, in order to "undo" the square root, you must SQUARE both sides of the equation.

+%283x%2B1%29%5E%281%2F2%29+=+4
sqrt%283x%2B1%29+=+4
3x%2B1+=+16
3x=15
x=5

Check:
%283%2A5%2B1%29%5E%281%2F2%29=4
16%5E%281%2F2%29=4
sqrt%2816%29=4
It checks!

For additional explanation on fractional exponents, please see my own website. You can find my website by doing a Google search for my name "Dr. Robert J. Rapalje". Look for "Rapalje Homepage", which should be the first item on the search. Once you find my homepage, for a written explanation, click on "Basic, Intermediate, and College Algebra: One Step at a Time." Look in Intermediate Algebra in Chapter 3 for Section 3.05 Fractional Exponents. There you will find a detailed explanation, and solutions!!

I have many other topics explained in this way from Basic, Intermediate, and College Algebra. Please check out my website to see what I have. It's all FREE, and if you send me an Email, I'll be glad to help you find something.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus