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. 
(c) ( 3x )^1/3

Accepted Answer

Hello, everyone. In this video, we're gonna be looking at this practice problem where we want to rewrite the expression six X to the power of 1/6 in radical form and evaluate. So in this case, recall, that radical form means that we're gonna have some sort of radical. But we can also arrive at that conclusion because we have this exponent that is a fraction. And whenever we have exponents that are fractions, we can convert them into a radical form. So say I have a to the one divided by N power, I can rewrite that as he ends route of A. And you can see how I now have a radical. So I went from a fraction exponent to a radical where the denominator of that fraction became the route I was taking. So in this case, the denominator was N. So I ended up taking the nth root of A. So we're gonna use this sort of logic to help us convert our expression into a radical. So here we have six X to the one sixth. And you can see that the denominator is six, which means I'll be taking the sixth route of the expression here, which is six X whenever you have this fraction because it's in the parentheses or outside the parentheses, it applies not only to the X but also to the six. So that's why we included six X inside of the radical. If it had been six times X to the 1/6 we would have to only worry about the fraction applying to X because the six would have an exponent of one. So this would look more like six times the sixth route of X. But again, our expression had the 1/6 power outside the parentheses, which meant we had to apply it to both the six and the X. And that's what we wrote inside this radical. So the sixth route of six X is actually our final answer because we can't simplify that any further. And you can see that, that aligns with answer choice C so hopefully, this video helped and see you next time.

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

Key Concepts

Rational Exponents

Radical Expressions

Properties of Exponents

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