Video Transcript
If the degree of seven 𝑥 to the
fifth power is the same as that of negative six 𝑦 to the power of 𝑛, what is the
value of 𝑛?
We’re given two algebraic
expressions. And we’re told that both of these
have the same degree. To answer this question, we first
need to find the degree of seven 𝑥 to the fifth power. We can see this is a monomial
because it’s one term and the exponent of 𝑥 is five, which is a positive
integer. Now, we could use the fact that
this is a polynomial to find the degree of this expression as a polynomial. However, we can also use an
equivalent definition because our expression only contains one term.
The degree of an algebraic term is
the sum of the exponents of all the variables in that term. And this will give us the same
answer as the degree of our polynomial because this has only one term. We can see the exponent of our
variable is five. Therefore, seven 𝑥 to the fifth
power is of degree five. But then, the question tells us
that negative six 𝑦 to the 𝑛th power has the same degree. So, it must also be of degree
five. And then, because this is also a
singular term, the sum of all the exponents of the variables must be equal to
five.
But we can see there’s only one
exponent on our variable, the unknown 𝑛. Therefore, to make seven 𝑥 to the
fifth power and negative six 𝑦 to the 𝑛th of power have the same degree, we must
have that 𝑛 is equal to five.
