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

-56a^12b^10c...

Question

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

-56a^12b^10c^8/7ab^2c^4

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 negative 81 A to the exponent 16 B to the exponent C to the exponent 10, divided by nine A B to the exponent six C cubed. We're given four answer choices. Option A is 1/9 multiplied by A to the exponent 15 B to the exponent eight C to the exponent seven. Option B is negative 1/9 A to the exponent 15 B to the exponent eight C to the exponent seven. Option C is nine A to the exponent B to the exponent eight C to the exponent seven. And option D is negative nine A to the exponent 15 B to the exponent eight and C to the exponent seven. Let's start by rewriting what we were given. We have negative 81 A to the exponent B to the exponent 14 C to the exponent divided by nine A B to the exponent 6 c cubed. And let's start with the coefficient in front, right? We have negative 81 divided by nine. So this is gonna give us a coefficient of -9. OK. So we've dealt with the coefficient. Now, we need to deal with the A B and C terms and recall our quotient rule of experiments. We have X to the exponent N divided by X to the exponent N, we can write this as X to the exponent M minus N. So when we divide two things with the same base, we can combine them into one term where the exponents are subtracted. So we have the exponent of the numerator minus the exponent of the denominator. If we apply this to our problem, we have a, to the exponent 16 divided by A. This is gonna give us A to the exponent 16 -1. A, the exponent of the numerator minus the exponent of the denominator. Then we move to our B term, we have B to the exponent 14 divided by B to the exponent six. This gives us B to the exponent 14 -6. And finally are C terms C to the exponent 10 divided by C cubed. We get C to the exponent 10 -3. So now we've done the hard part, we've done the division and we're left with just simplifying our expression, simplifying these exponents that we have. So we have negative 9 a to the exponent 16, -1 gives us A to the exponent 15, B to the Exponent 14 -6. That's gonna give us B to the exponent eight and C to the exponent 10 -3 gives us C to the exponent seven. And that's our simplified expression. OK. We can't simplify any further. The result we found using the quotient rule of exponents to do that division was negative nine A to the exponent 15 B to the exponent eight C to the exponent seven which corresponds with answer choice D. Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 15–24, divide using the quotient rule. -56a^12b^10c^8/7ab^2c^4

Key Concepts

Quotient Rule

Polynomial Division

Simplifying Rational Expressions

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