Find the value of 𝑛 if the degree
of the monomial negative 𝑥 to the power of 𝑛 𝑦 is six.
We recall the definition that the
degree of a monomial is the sum of the exponents of all included variables. We also note that constants have
the monomial degree of zero. The variable 𝑦 is the same as 𝑦
to the power of one. This means that the variable 𝑥 has
an exponent of 𝑛, and the variable 𝑦 has an exponent of one. We are told in the question that
the degree of the monomial is six. Therefore, 𝑛 plus one is equal to
six. Subtracting one from both sides of
this equation gives us 𝑛 is equal to five. The value of 𝑛 if the degree of
the monomial negative 𝑥 to the power of 𝑛 𝑦 is six is 𝑛 is equal to five.