Video: Identifying Monomials

Given that the expression 𝑥^(𝑎)𝑦^(𝑏) is a monomial, what must be true of the exponents 𝑎 and 𝑏? [A] 𝑎 and 𝑏 are both negative integers. [B] 𝑎 and 𝑏 are both nonnegative integers.

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Video Transcript

Given that the expression 𝑥 to the power of 𝑎 𝑦 to the power of 𝑏 is a monomial, what must be true of the exponents 𝑎 and 𝑏? Is it option A) 𝑎 and 𝑏 are both negative integers or option B) 𝑎 and 𝑏 are both nonnegative integers?

A monomial is an expression with just one term where all exponents or indices are nonnegative integers. This means that option B is our correct answer. The expression 𝑥 to the power of 𝑎 𝑦 to the power of 𝑏 is a monomial if and only if 𝑎 and 𝑏 are both nonnegative integers.

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