Question 307374
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.


{{{ (3x+1)^(1/2) = 4}}}
{{{sqrt(3x+1) = 4}}}
{{{3x+1 = 16}}}
{{{3x=15}}}
{{{x=5}}}


Check:  
{{{(3*5+1)^(1/2)=4}}}
{{{16^(1/2)=4}}}
{{{sqrt(16)=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