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

15x⁹/3x⁴

Question

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

15x⁹/3x⁴

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 given is 28 x to the exponent 14, divided by 7 x to the exponent eight. We have four answer choices. Option A four, X to the exponent six. Option B 1/4 x to the exponent six, option C four, X to the Exponent 22. And option D 1/4 X to the exponent 22. We're gonna start by rewriting the expression. We were given 28 X to the exponent 14 divided by 7 x to the exponent eight. And we can start by dividing these coefficients first. OK. So the coefficients just these numbers out in front. So we have 28 divided by seven, that's equal to four. So we get this coefficient of four and now we need to deal with our X terms. So recall the quotient rule of exponents. If we have two things divided that have the same base, we can write this as a single term where we have that same base and 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. Yes. So we take the exponent from the numerator subtract the exponent from the denominator. If we apply that to our problem, we have X to the exponent 14 divided by X to the exponent eight. We can write this as X to the exponent 14 -8. OK. Exponent of the numerator minus the exponent of the denominator is our new exponent. And now we've performed that division and we're left with just simplifying our exponent. So we have 4 x and the exponent is 14 -8, which we can simplify as six. And that's our simplified expression. We can't simplify it any further. That's the result we were hoping for. If we compare this to our answer choice, we used the quotient rule performed a vision on this expression and we found that the simplified expression was four X to the exponent six 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. 15x⁹/3x⁴

Key Concepts

Quotient Rule

Polynomial Division

Simplifying Expressions

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