Match the rational exponent expression in Column I with the equiv...

Question

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. 
(a) ( -3x )^1/3

Accepted Answer

Hello everyone in this video. We're going to be looking at this practice problem where we want to write the expression parentheses negative four and parentheses to the 1/4 in radical form and evaluate. So in this case we call that because we're looking for radical form. We need to have this radical in our final answer. And we can also sort of deduce that we're going to need a radical because we have this fraction exponent. So whenever there's a fraction exponent we can rewrite the expression using a radical. So say I have a to the power of one divided by nine. I can rewrite this in radical form by taking the denominator of that fraction and saying I will be taking the root of that. So in this case the denominator was n. So that means I'll be taking the and the root of this expression which is a So you can see how I started with a fraction and fraction in the exponent. And I ended up with a radical. So that's what we're going to try to do with our expression. And in this case we have negative for X to the 1/4. So if I try to rewrite this in radical form again I need the denominator which is four. So I'll be taking the fourth root of the expression here and notice how I'm not only taking the fourth root of X but also negative four because the 1/4 is outside of the parentheses. It applies not only to the ex but also to the -4. So that means that I need to write negative for X. Inside of my radical here and from this expression, you can see that we can't simplify the fourth root of negative four X any further. So this becomes our final answer. And you can see that that aligns with answer choice A. So flee. This video helped and see you next time.

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Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (a) ( -3x )^1/3