Final answer:
The degree of a monomial is the sum of the exponents of its variables. To find a in the monomial 3x²yᵃzᵃ with a degree of 10, we set up the equation 2 + a + a = 10 and solve for a.
Step-by-step explanation:
The degree of a monomial is the sum of the exponents of its variables.
In the given monomial 3x²yᵃzᵃ, the degree is 10. Since the degree is the sum of the exponents, x has an exponent of 2, y has an exponent of a, and z has an exponent of a. Therefore, we can write the equation: 2 + a + a = 10.
Simplifying the equation gives us 2a + 2 = 10. Subtracting 2 from both sides, we get 2a = 8. Dividing both sides by 2, we find that a = 4.