In Exercises 15–24, divide using the quotient rule.

x⁹y⁷/x⁴y²

Question

In Exercises 15–24, divide using the quotient rule.

x⁹y⁷/x⁴y²

Accepted Answer

Hey, everyone in this problem, we're asked to use the quotient rule of exponents to perform division in the given expression. The expression we're given is X to the exponent 12 Y to the exponent eight divided by X to the exponent nine Y to the exponent five. The answer choices were given are A X cubed, Y cubed B one divided by X cubed Y cubed C X cube Y N D X Y Q. We're gonna start by rewriting the expression we were given. So we have X to the exponent 12 Y to the exponent eight divided by X to the exponent nine Y to the exponent five. Now let's recall our potent rule of exponents. If we have two things with the same base that are being divided, we can write this as a single term with that original base where we subtract the exponents. OK. So if we have a, to the exponent M divided by A to the exponent N, we can write this as a to the exponent M minus N. So we take the exponent from the numerator and subtract the exponent from the denominator. Let's apply this to our problem starting with the X terms, we have X to the exponent 12 divided by X to the exponent nine. You can write this as a single term X to the exponent. While we take the exponent of the numerator, just 12 subtract the exponent from the denominator which is nine. So we have X to the exponent 12 minus nine and we can apply the same for the Y terms. So we get Y, we have Y to the exponent eight divided by Y to the exponent five. So we get Y to the exponent eight minus five. And now we've done the division, we've performed the division. All we need to do is simplify the exponents. We've found we have X to the exponent 12 -9. This gives us execute and we have Y to the exponent 8 -5 that gives us Y cubed. So we have X cubed. Why? Cute? And this is as simple as we can get this expression and we have a single X term, single Y term. Those exponents have been simplified. And so that is the result that we were hoping for if we compare this to our answer choices, OK. We use the quo rule. We found that the expression was equivalent to X cubed, Y cubed which corresponds with answer choice. A thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 15–24, divide using the quotient rule. x⁹y⁷/x⁴y²

Key Concepts

Quotient Rule

Simplifying Rational Expressions

Exponent Rules

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