Simplify each expression. See Example 1. (½ mn) (8m²n²)

Question

Accepted Answer

Welcome back. I am so glad you're here. We're told for the following polynomial expression, simplify our polynomial expression is the quantity of 1/5 HK multiplied by the quantity of K cubed each cubed. Our answer choices are answer choice A six H raise to the fourth K raise to the fourth answer. Choice B five H raise to the fourth K raise to the fourth answer trace C six H cubed K cubed and answer choice D five H cubed K cubed. All right. So we recall from previous lessons that when we are multiplying constant terms. So the 1/5 and the 30 we are going to just multiply those as normal, 1/5 multiplied by 30 gives us a positive six. But when we're multiplying variables that have exponents, we need to recall the rules of exponents. So we're calling the rule for multiplying variables with exponents. If we had M raised to the A power multiplied by M raised to the B power, we see we have the same base here. The M is the same base. What we're going to do is add our exponents and it will equal that M that same base raised to the A plus B. So here we have HS which are the same base. We have an H raised to an invisible first power and an H raised to a third power or cubed. So we can put, we can put one more layer of work. We have H raised to the first H cubed. And then we have these KS that are the same base. The first one is K raised to the 1st, 1st power. And the second one is K cubed. So we can put down here A K raised to the first multiplied by K cubed. And now we get to add the exponents of the like bases. So for H rays to the first multiplied by H cubed, we're going to add one plus three and one plus three equals four. So this will give us, we'll bring down our six and then we'll have H raises to the fourth power. And then very similarly with our KS, we have K raise to the first multiplied by K cubed. One plus three is still four. So we have six a trays to the fourth K rays to the fourth. And that is our answer. Simplified. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Simplify each expression. See Example 1. (½ mn) (8m²n²)

Key Concepts

Multiplication of Algebraic Expressions

Properties of Exponents

Simplifying Numerical Coefficients

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