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. (z^3/4)/(z^5/4)(z^-2)

Accepted Answer

Hey everyone in this problem we are asked to solve the given expression that the answer should be written without negative exponents. We're being told that the variable shown are all belonging to the positive real numbers were given the expression Q. To the exponent 5/6 divided by Q. To the exponent negative 13/6 times Q. Two exponents three. So let's just write this out. Q. To the exponent 5/6. All divided by Q. To the exponents negative 13/6 times Q. Two. Exponents three. Okay. All right, so you can go about this a couple of different weights. Okay? Whatever order you want to deal with these, I'm gonna start by doing the multiplication in the denominator. Okay we have two things multiplied together that have the same base. So let's deal with that first. Okay and recall that if we have two things multiplied together with the same base. So A. To the exponent M times A. To the exponent end. Okay we can simplify this and write this as A. To the exponent. M plus N. Okay, so we add the exponents. Alright so applying this in our denominator and the numerator stays the same queue to the exponents 5/6 divided by Q. To the exponents negative 13/6 plus three. So we have the first exponent plus the second exponent and if we simplify this. Okay We're gonna end up with Q. to the exponent 5/6 divided by Q. Two. The exponents we have negative 13 divided by six plus three. Now three. If we want to find a common denominator Okay, three is going to be equal to 18/6. So we have negative 13/6 plus 18/6. That's going to give us 5/6. Okay? So if Q to the exponent five or six divided by Q. To the exponent five or six. Okay? You might notice right away. We have something divided by the exact same something so that's going to be equal to one. Ok, let's show why that's true using our exponent rules. Okay? So if we have two things divided by each other and they have the same base. So we have a to the exponent M divided by A to the exponent end. Recall that we can write this as a to the exponent m minus end. Okay, so when we're dividing with the same base, we can simplify this into one single base where we subtract the exponents. Okay, so if we do that we end up with Q to the exponent 5/ -5/6. Well that's equal to Q. To the exponent zero, which is equal to one. Ok, so if you notice right off the bat that this was equal to one, that's great. Um but it's good to write out this work and kind of see why that works with our exponent rules. Okay. All right. So if we're looking at our answer choices, we see that the simplified version of the expression is going to be a one. Thanks everyone for watching. I hope this video helped see you in the next one.

Struggling with College Algebra?

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (z^3/4)/(z^5/4)(z^-2)

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