Video: Finding the Missing Constant Given the Degree of the Monomial

Find the value of 𝑛 if the degree of the monomial (−𝑥^𝑛 𝑦) is 6.

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Video Transcript

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.

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