Chapter 8.1, Problem 1P

(a)

To determine

To find: the degree of the monomial $8xy$

Answer to Problem 1P

Degree of the monomial $8xy$ is 2 $$

Explanation of Solution

Given information:

Given monomial is $8xy$

Formula Used:

The degree of the monomial is the sum of the exponents of all included variables.

The variables in $8xy$ are x and y. Each one has exponent 1

  $8xy$ = $8x^1{y}^1$

Degree = Exponent of x + Exponent of y$=1+1=2$

∴Degree of the monomial $8xy$ is 2

(b)

To determine

To find: the degree of the monomial $-7y^{4}z$

Answer to Problem 1P

Degree of the monomial $-7y^{4}z$ is 5

Explanation of Solution

Given information:

Given monomial is $-7y^{4}z$

Formula Used:

The degree of the monomial is the sum of the exponents of all included variables.

The variables in $-7y^{4}z$ are y and z.

  $-7y^{4}z=-7y^4{z}^1$

Exponent of y is 4 and exponent of z is 1

Degree = Exponent of y + Exponent of z$=4+1=5$

∴Degree of the monomial $-7y^{4}z$ is 5

(c)

To determine

To find: the degree of the monomial 11 $-7y^{4}z$

Answer to Problem 1P

Degree of the monomial 11 is 0

Explanation of Solution

Given information:

Given monomial is 11

Formula Used:

The degree of the monomial is the sum of the exponents of all included variables.

There is no variable in the given monomial 11.

Since the degree of a nonzero constant is zero.

∴Degree of the monomial 11 is 0