Question Video: Simplifying Algebraic Expressions Using Laws of Exponents Mathematics

Video Transcript

Simplify six 𝑥 squared 𝑦 squared times negative nine 𝑥 squared 𝑦 to the fifth power.

Here, we’re finding the product of two monomials. And so, we recall the process for multiplying two or more monomials. We begin by multiplying the coefficients of each term. And then we separately multiply the variables. Now, we will need to use the laws of exponents to do so. The specific law that we’re going to use is the fact that when the bases are the same, we’d multiply exponential terms by just adding the exponents. So, 𝑥 to the power of 𝑎 times 𝑥 to the power of 𝑏 is 𝑥 to the power of 𝑎 plus 𝑏. Let’s identify the coefficients in our product. We have six here and negative nine here, and so we’re going to multiply six by negative nine. Six times nine is 54. And a positive multiplied by a negative is a negative, so six times negative nine is negative 54.

Next, we multiply the variables. We’re going to multiply 𝑥 squared by 𝑥 squared. And of course, to do so, we simply add the exponents. So, we get 𝑥 to the power of two plus two, which is, of course, the same as 𝑥 to the fourth power. There’s another variable we need to consider though, and that’s 𝑦. So, we do the same with this one. 𝑦 squared times 𝑦 to the fifth power is the same as 𝑦 to the power of two plus five. And of course, since two plus five is seven, 𝑦 squared times 𝑦 to the fifth power is 𝑦 to the seventh power. When we combine all of this, we get the result of multiplying six 𝑥 squared 𝑦 squared by negative nine 𝑥 squared 𝑦 to the fifth power. It’s negative 54𝑥 to the fourth power 𝑦 to the seventh power.