Math Snap

STEP 1

1. The degree of a term in a polynomial is the sum of the exponents of the variables in that term.
2. The degree of a polynomial is the highest degree of any term in the polynomial.

STEP 2

1. Identify the degree of each term in the polynomial.
2. Determine the degree of the polynomial.
3. Identify the degree of the first term, $2ab^9$.

STEP 3

Identify the degree of each term in the polynomial:
- For the term $2ab^9$, the degree is the sum of the exponents of $a$ and $b$. Here, $a$ has an exponent of 1 and $b$ has an exponent of 9.
$$\text{Degree of } 2ab^9 = 1 + 9 = 10$$

STEP 4

- For the term $-8a^7$, the degree is the exponent of $a$, which is 7.
$$\text{Degree of } -8a^7 = 7$$

STEP 5

- For the term $8b^2$, the degree is the exponent of $b$, which is 2.
$$\text{Degree of } 8b^2 = 2$$

STEP 6

- For the constant term $-6$, the degree is 0 because there are no variables.
$$\text{Degree of } -6 = 0$$

STEP 7

Determine the degree of the polynomial by identifying the highest degree among all the terms:
The degrees of the terms are 10, 7, 2, and 0. The highest degree is 10.
$$\text{Degree of the polynomial} = 10$$

Identify the degree of the first term, $2ab^9$:
As calculated earlier, the degree of $2ab^9$ is 10.
$$\text{Degree of the first term} = \boxed{10}$$ The degree of the first term, $2ab^9$, is $\boxed{10}$.