Simplify each expression. See Example 1. (3y^4)(-6y^3)

Question

Accepted Answer

Hey everyone here we are asked to reduce the following expression to its simplest form where we have the quantity of four X to the six power times the quantity of negative eight X squared. So now our first step here in simplifying this expression is to just collect the coefficients and the variables together. So doing this beginning with our coefficients, we have the quantity of four times negative eight. And now grouping together our X variables. We have the coefficient times the quantity of X to the six power times X squared. So now we just need to work to simplify this expression and we can do this by first multiplying our coefficients together. So we have four times negative eight which gives us negative 32. So our expression becomes negative 32 times the quantity of X to the six power times X squared. So now we just need to reduce our X variables here and we can do this by recalling the product rule of exponents which tells us that A to the power of M times A to the power of N is equivalent to A to the power of M plus n. So here, since we are multiplying exponents with the same base, we can apply this rule, this product rule. So doing this, we can rewrite our expression as negative 32 times the quantity of X to the power of six plus two. So now all that is left to do is to simplify our exponents here and we see our final simplified expression becomes negative times X to the power of six plus two, which is just eight. So now we have found our final simplified form and we are left with answer choice. A thanks for watching. I hope you found this video helpful, and I'll see you again next time.

Simplify each expression. See Example 1. (3y^4)(-6y^3)

Key Concepts

Multiplication of Monomials

Properties of Exponents

Simplifying Expressions

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