In Exercises 1–8, multiply the monomials.

(3x²)(5x⁴)

Question

In Exercises 1–8, multiply the monomials.

(3x²)(5x⁴)

Accepted Answer

Hey, everyone in this problem, we're asked to perform multiplication. For the given monos, we have 7 x cubed multiplied by nine X to the exponent five. We're given four answer choices. Option A 63 X to the exponent 15. Option B 16 X to the exponent eight, option C 16 X to the exponent 15. And option D 63 x to the exponent eight, we're gonna start by rewriting the mo monos that we were given. So we have seven, execute the first one multiplied by nine X to the exponent five. And we're asked to multiply these. Let's start with the coefficient here. So we have this constant seven in our first term multiplied by nine in our second mo mono. So for our coefficient, we have seven multiplied by nine. And then we need to deal with the X terms. We have X cubed multiplied by X to the exponent five. Recall that if we have two things multiplied together with the same base, say A to the exponent M multiplied by A to the exponent N, we can write this as A to the exponent M plus X. Yeah. So if they have the same base. And we, we're multiplying them, we can combine this into one term where the exponents get at it. If we apply that to our case, we have X cubed multiplied by X to the five, we can write this as X to the exponent 3-plus 5. And now we've performed the multiplication. We have some simplifying to do seven multiplied by nine, gives us 63. And we can simplify in our exponent X to the exponent three plus five is equal to X to the exponent eight. So we have 63 x to the exponent eight. That is the result of multiplying the monos we were given. If we compare this to our answer choices, this corresponds with answer choice. D Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 1–8, multiply the monomials. (3x²)(5x⁴)

Concetti chiave

Monomials

Multiplication of Monomials

Exponent Rules

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