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. Today we're going to be rewriting the given expression into its radical form. So what we are given is eight times the quantity X to the power of negative 1/8. Now before we rewrite this in this radical form let's go ahead and turn the negative exponents into a positive exponent. Let's suppose that we have X. To the power of negative A. If we wanted to turn the exponent positive we're going to place the value of X to the power of a under one. So we can rewrite this as one over X. To the power of A. And that's how we can rewrite the given exponential value into a positive exponential value. So if we apply this rule to X to the power of negative 1/8, we can rewrite the expression as eight times one over X. To the power of positive 1/8. Okay, now that we have a positive exponential value, let's go ahead and recall the rule in rewriting an exponent into its radical form. Let's suppose that we have X. To the power of a over N. If we wanted to rewrite this into a radical form, we can rewrite it as the end through of X. To the power of A. This is where the numerator of the current exponent becomes the innermost exponent of the radical form and the denominator of the exponents becomes the 10th route of the argument. So here for extra power of 1/8 A is going equal to one and n is going to equal to eight. So X to the power of 1/8 can be rewritten as the eighth route of X to the power of one and X to the power of one is just going to evaluate to give us X. So what we are left with is the eighth root of X. So if we replace the denominator with the eighth root of X, what we are left with is eight times one over the eighth root of X. Now, all we need to do is multiply the values together and multiplying eight with one over the eight root of X is going to give us eight over the eighth route of X. And this is going to be the simplified form of the given expression. And with that being said, the answer to this problem is going to be be So I hope this video helps you in understanding how to approach this problem and I'll go ahead and see you all in the next video

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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. (c) 3x^-1/3

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