Simplify each expression. Write answers without negative exponent...

Question

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (k^1/3)/(k^2/3)(k^-1)

Accepted Answer

Hey, everyone in this problem, we're asked to solve the given expression and the answer should be written without negative exponents. And we're told that all variables shown belong to the positive real numbers. And the expression we're given is Q to the exponent 1/7 divided by Q to the exponent negative 6/7 times Q. So writing this out Q to the exponent 1/7 divided by Q to the exponent negative 6/7 times Q. All right. So we can deal with this in a couple of different ways to the order that you approach this. I'm gonna start by simplifying the denominator. OK? We have two things multiplied together that have the same base. So let's deal with that first. OK. Now our call, if we have two things multiplied together with the same base A to the exponent M times A to the exponent N, then our exponent rules tell us that this is equal to A, to the exponent M plus N. OK. So we add the exponents together. So in the denominator, we have Q to the exponent 1/7 in the nummi numerator. OK. And then in the denominator, we get Q to the exponent negative 6/7 plus one. OK. So the exponent of the first term and the exponent of the second term added together. All right, if we simplify this Q to the exponent 1/7 in the numerator, Q to the exponent negative 6/7 plus one, it's just gonna be 1/7. Now, you might notice right away, we have Q to the exponent 1/7 divided by Q to the exponent 1/7. OK? Something divided by the exact same something is gonna give us one. OK. Let's use our exponent rules to just show why. That's true. All right. So let's recall if we have two things that are being divided and they have the same base. What happens? Well, our exponent rules tell us that if we have a, to the exponent M divided by A, to the exponent N, this is going to be equal to A, to the exponent M minus N. OK? So when they were multiplied together, we add the exponents now that they're divided, we're gonna subtract the exponents. OK? So this is gonna give us Q to the exponent 1/7 minus 1/7. OK. The exponent of the numerator minus the exponent of the denominator, this is Q to the exponent zero and we know anything to the exponent zero is going to be equal to one. So it does indeed equal one. OK. And we've just used our exponent rules to show that um from the step above where we had Q to the exponent 1/7, divided by Q to the exponent 1/7. All right. So if we look at our answer traces, we see that the solution to the expression we were given is going to be a one. Thanks everyone for watching. I hope this video helped see you in the next one.

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Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (k^1/3)/(k^2/3)(k^-1)

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