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. 
(b) ( -3x )^-1/3

Accepted Answer

Hello everyone in this video. We're going to be looking at this practice problem where we want to rewrite the expression parentheses negative five X. And parentheses to the negative 1/5 in radical form and evaluate. So because the question is asking us to write it in radical form, we know that there's going to be some sort of radical but we can also reduce that or deduce that from the exponent being a fraction. So whenever the exponents of a number or component is a fraction we know that we can rewrite it as a radical and in this case there's also a negative exponents. So we can also express a negative exponents as a fraction. So let's look at that scenario first. So say I have a negative exponent. I'll say a to the negative end. I can rewrite this as a fraction as one divided by A. To the N. And notice how in the denominator the N. Is now positive instead of being negative. So by rewriting it in the denominator I changed it from negative to positive. And now we can look at if it was a fraction. So say I have W To the power of one divided by Z. I can rewrite this as a radical by saying this Z route of w. So notice how the denominator in the fraction became the route I was taking. So Z was the denominator. So I'll be taking the easy route of W. So we're going to use these two rules to help us rewrite our expression in radical form. And the first thing we can do is Change negative 1/5 into a positive exponent. And we're going to do that by converting this into a fraction. So this would become now one divided by negative five X. To the positive 1/5. And notice how the whole expression negative five X. Is in the denominator. Now because of this parentheses that negative 1/5 applies not only to the X, but also to the negative five. So that means that whole expression needs to be expressed in the denominator. Well now we have a positive exponent but we still don't have a radical. So that's where we need to convert the negative five X To the 1/5 into radical form. And in this case remember we need to do the denominator Is the route we're taking. Which in this case it's the fifth root because the denominator is five. And once again we have to pull the whole expression because the 1/5 applies not only to the X, but also to the negative five. So we're taking the fifth root of negative five X. So once we evaluated this, this doesn't become our final answer, we need to play it back into the fraction. So this becomes one divided by the 5th root Of -5 X. And you can see that we can't simplify this any further. So this becomes our final answer and you can see that answer, choice B also has one divided by the fifth root of negative five X. So B is also our final answer, 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. (b) ( -3x )^-1/3

Key Concepts

Rational Exponents

Radical Expressions

Reciprocal of a Number

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