Question

Give the degree of the monomials: 8X³Y⁴Z, 45G⁵H⁶, -17MN³, A⁶BC⁷, 4P⁷O⁸U³.

a) 3, 5, 3, 8, 15
b) 7, 11, 6, 14, 15
c) 8, 6, 3, 13, 15
d) 10, 11, 7, 12, 15

Answer 1

The degrees of the given monomials are 8, 11, 4, 14, and 18 respectively. None of the provided answer choices are correct.

Step-by-step explanation:

The degree of a monomial is the sum of the exponents of all its variables. To find the degree, we simply add up the exponents of each variable in the monomial.

1. For 8X³Y⁴Z, the degree is 3 (from X³) + 4 (from Y⁴) + 1 (from Z), which gives us a degree of 8.
2. For 45G⁵H⁶, the degree is 5 (from G⁵) + 6 (from H⁶), which gives us 11.
3. For -17MN³, the degree is 1 (from M) + 3 (from N³), and that totals 4.
4. For A⁶BC⁷, the degree is 6 (from A⁶) + 1 (from B) + 7 (from C⁷), equaling 14.
5. For 4P⁷O⁸U³, the degree is 7 (from P⁷) + 8 (from O⁸) + 3 (from U³), which gives us 18.

Therefore, the degrees of the given monomials are 8, 11, 4, 14, and 18, respectively. None of the provided options (a, b, c, d) correctly matches these degrees.