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.
