In Exercises 1–14, multiply using the product rule.

(-3x⁴y⁰z)(-7...

Question

In Exercises 1–14, multiply using the product rule.

(-3x⁴y⁰z)(-7xyz³)

Accepted Answer

Hey, everyone in this problem, we're asked to use the product rule of exponents to simplify the expression. The expression we given is negative 10 A to the exponent zero BC cubed multiplied by negative eight A B to the exponent five C. We're given four answer choices. Option A negative 80 A to the exponent six BC to the exponent four. Option B 80 B to the exponent six C to the exponent four. Option C negative 80 A to the exponent six B to the exponent four C. And option D 80 A B to the exponent six C to the exponent four. We're gonna start by rewriting the expression we were given. So we have negative 10 A to the exponent zero BC Q multiplied by -8 A B to the exponent five C. So we're gonna multiply these together and let's start with the coefficient. OK. So just that constant coefficient, that number out front. So we have negative 10 multiplied by -8. We're gonna write those first negative 10 multiplied by -8. And we're gonna try to group these terms together. Now we're multiplying A to the exponent zero by A. Now OK. So what does the product rule of exponents tell us? Well, recall if we have two things multiplied together, that have the same base, we can write this as a single term with that same base where the exponents of the original terms get added together. OK. So if we have X to the exponent M multiplied by X to the exponent N, we can write this as X to the exponent M plus N. So applying this to our A terms A, to the exponent zero multiplied by A, it's gonna give us A to the exponent zero plus one. Then we add the two stocks, we can apply the same rule to our B terms. So we have B multiplied by B to the exponent five. It's gonna be B to the exponent one plus, right can recall if there's no exponent, it's just a perceived one. So A B to the exponent one plus five and then we have C cubed multiplied by C. This is gonna give us C to the exponent three plus one, the same base at the exponents. So now we grouped all of these terms together and we can go ahead and simplify our expression or constant. We have negative 10 multiplied by -8. This gives us 80 A to the exponent zero plus one, gives us a, A to the exponent one where we can write that as just A B to the exponent one plus five gives us B to the exponent six and C to the exponent three plus one gives us C to the exponent four. Now, we can't simplify this expression any further. So this is the result we were looking for. If we compare this to our answer choices, we found using the product rule of exponents that the simplified expression is 80 A B to the exponent six C to the exponent four, which corresponds with answer choice D. Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 1–14, multiply using the product rule. (-3x⁴y⁰z)(-7xyz³)

Key Concepts

Product Rule

Exponents

Coefficients

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