Find each product. Assume all variables represent positive real n...

Question

Find each product. Assume all variables represent positive real numbers. y^5/8(y^3/8-10y^11/8)

Accepted Answer

Welcome back. I am so glad you're here. We are given the expression A to the 3/14 C times A to the 5/14 minus 12 A to the 11 14th. So and we are asked to determine the product or in other words to multiply what we're going to be multiplying is we're going to be distributing this a to the 3/14 times the two terms inside the parentheses. So we will be taking A to the 3/ times A to the 5/14. So and we will be taking A to the 3/14 so times negative A to the 11 14 months. And we will add those two together. Alright. We recall from previous lessons that when we have variables with the same base so they both got this A and we are multiplying them together and they have exponents. We are going to take those exponents and we are going to add them together and then the base will remain the same. So we'll still have an A. When we multiply A to the 3/14 times A to the 5/ but we're going to add those exponents together to get our new exponents. So we'll be taking 3/14 c plus 5/14. So we have a common denominator so we can add the numerator is three plus five equals eight. So 8/14. So and those are both divisible by 28 and 14. So this reduces to eight divided by two is 4/14 divided by two is seven. So a two the 4/7 and now we can bring down this plus and we're going to have a to the 3/14 times negative 12. 8 to 11 14th. So while that negative 12 can come down, that's just being multiplied by an invisible one in front of the A. To the 3/14 1 times negative 12 is negative 12. So we've got that negative 12. But now let's figure out this A when we're going to multiply A to the 3/14 C times A. To the 11 14 months. And again we are going to add those exponents together. So three plus 14 in the numerator is because we have a common denominator, three plus 14 is 14. We have 14 14th which equals one. So we have a two. The first down here A. To the first is just A. We don't need to put the to the first so we've got a two the 4/7 and then we don't have to put plus minus. We can put minus 12 A. We look at our answer choices in this matches with answer choice. A. Well done, we'll catch you on the next one

Find each product. Assume all variables represent positive real numbers. y^5/8(y^3/8-10y^11/8)

Key Concepts

Exponents and Powers

Factoring Expressions

Polynomial Operations

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