Video Transcript
Find the degree of the monomial
negative three 𝑥 raised to the fifth power. Find the degree of the monomial
seven 𝑥𝑦𝑧 squared.
In this question, we are given two
different monomials and asked to find the degree of each of these monomials. To answer this question, we can
begin by recalling what we mean by the degree of a monomial. It is the sum of the exponents of
all of the variables in the monomial.
There are several important things
to note about this definition. First, if there is only a single
variable in the monomial, say 𝑥, then we have 𝑎𝑥 raised to the power of 𝑛, where
𝑎 is nonzero. In this case, we say that the
degree of the monomial is the exponent of 𝑥, which is 𝑛. Second, we say that the degree of
any nonzero constant is one. Finally, we leave the degree of
zero undefined, though some people like to define this as negative one or even
sometimes negative ∞.
We can use this definition to find
the degree of the two given monomials. In the first monomial, we see that
there is only a single variable, 𝑥. In cases like this, we know that
the degree of the monomial is equal to the exponent of the variable. So the degree of negative three 𝑥
raised to the fifth power is five.
For the second monomial, we can see
that there are three variables: 𝑥, 𝑦, and 𝑧. We know that the degree of the
monomial is the sum of the exponents of its variables, so we can rewrite 𝑥 and 𝑦
as 𝑥 raised to the first power and 𝑦 raised to the first power to see that the
degree of this monomial is one plus one plus two, which is equal to four.
Hence, the degree of negative three
𝑥 raised to the fifth power is five, and the degree of seven 𝑥𝑦𝑧 squared is
four.
