Simplify each expression. See Example 1. (5x²y) (-3x³y⁴)

Question

Accepted Answer

Welcome back. I am so glad you're here. We're asked for the following polynomial expression to simplify our polynomial expression is the quantity of eight M raised to the fifth power H squared multiplied by the quantity of negative seven M cubed H cubed. Our answer choices are answer choice am raised to the 15th power H raised to the sixth power answer choice BM squared H raised to the negative one answer choice C negative 56 M raised to the eighth power H raise to the fifth power and answer choice. D negative 56 M raise to the 15th power H raised to the sixth power. All right. So we recall from previous lessons when we are multiplying just regular constant terms like this eight multiplied by negative seven. We're just going to multiply those eight multiplied by negative or yes, eight multiplied by negative seven is negative 56. But when we are multiplying variables with like bases, we are going to recall those rules for exponents. So if we had X raised to the A power multiplied by X raised to the B power, they have the same base the X and what we're going to do with their exponents is add them together. So this will equal X raised to the A plus B. So these MS have the same base. So that's going to remain the M and we can write out one more step. So we'll have M raised to the fifth multiplied by M cubed. And then as we said, we'll be adding those exponents together. So five plus three and five plus three is eight. So bringing this down, we have negative 56 M raised to the eighth power. Now these HS are also similar bases. We've got an H squared multiplied by an H cubed. We get to add the two plus three, those exponents two plus three is five. So this reads negative 56 M raised to the eighth power H raised to the fifth power. And that is our expression simplified. We look at our answer choices and this matches with answer choice. C well done. We'll catch you on the next one.

Simplify each expression. See Example 1. (5x²y) (-3x³y⁴)

Key Concepts

Multiplication of Coefficients

Product of Powers Property

Combining Like Variables

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