How to determine the numerical coefficients in an expressions?

Problem 1.

Determine the numerical coefficient of each term in the following expression

88a^{7} + 77b^{6}

First, see Definition of numerical coefficients.

The first term

88a^{7} = 88 * a^{7}

88 is the numerical coefficient. The a^{7} is a variable. The 7 is the exponent.

The second term

77b^{6} = 77 * b^{6}

77 is the numerical coefficient. The b^{6} is a variable. The 6 is the exponent.

Problem 2.

Determine the numerical coefficient of each term in the following expression

2.5a^{9} + b^{8}

The first term

2.5a^{9} = 2.5 * a^{9}

The 2.5 is the numerical coefficient. The a^{9} is a variable. The 9 is the exponent.

The second term

b^{8} = 1 * b^{8}

The 1 is the numerical coefficient. The b^{8} is a variable. The 8 is the exponent.

Problem 3.

Determine the numerical coefficient of each term in the following expression

-0.5a^{55} - b^{33}

Determine the numerical coefficient of the first term

-0.5a^{55} =

-0.5 * a^{55}

-0.5 * a

The negative fraction -0.5 is the numerical coefficient. The a^{55} is a variable. The 55 is the exponent.

Determine the numerical coefficient of the second term

-b^{33} = -1 * b^{33}

The negative number -1 is the numerical coefficient. The b^{33} is a variable. The 33 is the exponent.

Problem 4.

Determine the numerical coefficient of each term in the following expression

(6a^{17})/(18a) - b^{4}/84

Solution.

Determine the numerical coefficient of the first term

(6a^{17})/(18a) =

(6/18) * (a^{17}/a) =

6/(3 * 6)) * (a^{17 - 1}) =

(1/3) * a^{16}

(6/18) * (a

6/(3 * 6)) * (a

(1/3) * a

The 1/3 is the numerical coefficient. The a^{16} is a variable. The 16 is the exponent.

Determine the numerical coefficient of the second term. It is negative

-b^{4}/84 =

(-1 * b^{4})/84 =

(-1/84) * b^{4}

(-1 * b

(-1/84) * b

The negative factor -1/84 is the numerical coefficient. The b^{4} is a variable. The 4 is the exponent.