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

Question

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. 
(d) ( 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 six X. And parentheses to the power of negative 1/6 in radical form and evaluate. So in this case you can see that we might be using radical form because the question asked for radical form. But also there's a fraction as an exponent. Which means that we can represent that in radical form. Because when you think of a variable I'll say A To the power of one divided by nine. And a fraction. I can rewrite this as the end route of a. So you can see that when variables have exponents that are fractions. I can rewrite in radical form by taking the denominator and making that the route that I'm taking. So in this case the denominator was N. So that means I'm taking the route of A. And we can apply this same sort of logic to our expression. So in this case we have six sex. And that whole Expression is to the power of -1 6th. Well in this case we have to deal with this negative first. But recall that if we have a negative exponent I'll do another example say B. To the negative W. I can get rid of the negative by rewriting this as a fraction and expressing it in the denominator. So B. To the negative W. Can become positive by writing it as one divided by B. To the W. And notice how in the denominator the negative goes away. So for our expression if I rewrite six X to the negative 1/6. In a fraction form I can say it's the same as one divided by six X. To the positive 1/6. And now we have a positive exponent and I can make it a radical. So in order to make it radical I'm just going to look at six X. To the 1/6. And in this case you can see that I will be taking the six through Of this whole expression because this exponent applies to the six and the X. So that means I need to take the 6th root of six X. So now I have a radical and I need to reintegrate it into my fraction. So this becomes one divided by the 6th root of six x. And you can see that we can't really simplify this any further. So my final answer ends up being this fraction with the radical in the denominator and you can see that this aligns with answer choice B. One divided by the sixth route of six X. 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. (d) ( 3x )^-1/3

Verified Solution

Key Concepts

Rational Exponents

Radical Expressions

Reciprocal of a Number