Exercises 108–110 will help you prepare for the material covered ...

Question

Exercises 108–110 will help you prepare for the material covered in the next section.Multiply: (2x³y²)(5x⁴y⁷).

Accepted Answer

Hey, everyone in this problem, we're asked to perform multiplication. The expression we're given is nine X to the exponent five Y cubed multiplied by two X squared Y to the exponent seven. We're given four answer choices. Option A 18 X cubed Y to the exponent 10. Option B 18 XX to the exponent seven Y to the exponent 10. Option C 18 X to the exponent seven Y to the exponent 21. And option D 18 X to the exponent seven Y to the exponent negative four. We're gonna start by rewriting the expression we were given we have 9 x to the exponent five. Why cute multiplied by two X squared Y to the exponent 7th. I'm gonna start by multiplying the coefficient. So in the first term, we have a coefficient of nine and in the next one, we have a coefficient of two. So nine multiplied by two is going to give us a coefficient of 18. Then we're gonna move to the X terms we have X to the exponent five multiplied by X squared. Now recall if you have two things multiplied together with the same base, say A to the exponent M multiplied by A, to the exponent N, you can write this as a to the exponent M plus N. OK. So two things multiplied together with the same base. You can write that as one term where the exponent is the original exponents added together. OK. So here we have X to the exponent five multiplied by X squared, we can write this as X to the exponent five plus two. We do the same for the Y term. So we have Y cubed multiplied by Y to the exponent seven can write this as Y to the exponent three plus seven. So now we've done this multiplication and we're left with simplifying our exponents. We have the coefficient of 18 X to the exponent 5-plus 2. This is X to the exponent seven and we have Y to the exponent three plus seven, that's Y to the exponent 10. And this is as simplified as we can make this expression. So the result of our multiplication is 18 x to the exponent seven, Y to the exponent 10 which corresponds with answer choice. Beef. Thanks everyone for watching. I hope this video helped see you in the next one.

Struggling with College Algebra?

Exercises 108–110 will help you prepare for the material covered in the next section.Multiply: (2x³y²)(5x⁴y⁷).

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