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

50x²y⁷/5xy⁴

Question

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

50x²y⁷/5xy⁴

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 were given is 75 X to the exponent four Y to the exponent 17 divided by 15 X Y to the exponent 12. We're given four answer choices. Option A is 1/5 X Q Y to the exponent five. Option B is five X cubed, Y to the exponent five. Option C is one fif X to the exponent five Y Q and option D is 7 x cubed y to the exponent five. We're gonna start by rewriting the expression we were given. So we have 75 X to the exponent four Y to the exponent 17 divided by 15 X Y to the exponent 12. Let's start with the constant. So let's start with that coefficient imprint. We have 75 divided by 15. This is gonna give us a value of five. So we know that we're gonna have a coefficient of five. Now we have to figure out how to simplify this division amongst our X and Y terms what we call the quotient rule of experiments. If we have A to the exponent M divided by A to the exponent N. So we're dividing two terms that have the same base, then this is equal to writing A to the exponent M minus N. OK. So we divide two things with the same base. We can write this as a single term. We use that same base. And the exponent is gonna be the exponent of the numerator originally minus the exponent of the original denominator. If we apply this to our propel, and let's look at our X terms, we have X to the exponent four divided by X. So we can write this as a single term with the base X. And then we have the exponent, the exponent of the numerator, which was four minus the exponent of the denominator, which is one. So we get X to the exponent 4 -1. And we're gonna do the same thing for our Y term. We have Y to the exponent 17 divided by Y to the exponent 12. So we're gonna have the same base of Y. We're gonna take the exponent of the numerator 17, subtract the exponent of the denominator 12. So we have Y to the exponent 17 minus 12. So now we've done the division step here. Now we're left with just simplifying this expression. So we have five X to the exponent 4 -1, gives us X cubed. And why to the exponents? 17 -12 gives us Y to the exponent five, our exponents have been simplified, we just have one X term, one Y term, one constant coefficient. And so this is as simplified as we can get it. And that's the result we were looking for. If we compare this with our answer choices, we found using the quotient rule of exponents to perform division. The simplified version of this expression is five X cubed Y to the exponent five which corresponds with answer choice B thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 15–24, divide using the quotient rule. 50x²y⁷/5xy⁴

Key Concepts

Quotient Rule

Simplifying Rational Expressions

Exponents and Their Properties

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