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 write negative seven times X. To the negative 1/7 in its radical form and then evaluate that expression. So in this case whenever you see radical form or call that we're going to have some sort of square root in our radical form. So when we look at this problem or this expression you can see that there's no square root but we want to integrate the square root to return it to its radical form. But first let's deal with this negative exponent. So recall that if you have an exponents say I have X to the negative B. I can rewrite this as a fraction where this becomes one divided by X to the B. And notice how the exponent went from negative to positive by putting it in the denominator. So I'm gonna do that for my expression. So negative seven times X. To the negative 1/7 will become negative seven divided by X. To the 1/7. And notice how only the X component of this expression went into the denominator and not the negative seven. And that's because the negative seven has a positive exponent. We can say that there's a positive one as the exponent for negative seven. So it's going to remain in the numerator. But we've now rewritten this expression in fraction form but we still don't have this radical or the square root. Well whenever we have a fraction as the exponent call that we can rewrite that in radical form. So say I have X to the one over N. I can rewrite that as the end route of X. So notice how the denominator of the fraction became the route that I'm taking of the variable X. So once again I'm going to apply that to X to the one Next to the power of 1/7. And if I do that I'm taking the seventh route of X. And I can go ahead and substitute in The 7th Root of X into my denominator. So if I do that this becomes negative seven divided by the 7th route of X. And from here you can see that I can't simplify between the numerator and the denominator. So this becomes my final answer for this problem. And you can see that answer choice A. Also has negative seven divided by the seventh root of X. So answer choice A is 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

Negative Exponents

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