Division of a Monomial by a Monomial –
To divide one monomial by another, divide the numerical coefficient of the dividend by the numerical coefficient of the divisor and the powers of variables in the dividend by the corresponding powers in the divisor. Then multiply all the quotients.
Quotient of two monomials = (quotient of numerical factors) X (quotient of literal factors)
There are some example are given below for your better understanding -
Example.1) Divide 24x²y⁵ by 8xy
Ans.) As per the given condition, we have to 24x²y⁵ ÷ 8xy
24x²y⁵ 24
So, 24x²y⁵ ÷ 8xy = ---------- = -------- x²⁻¹ y⁵⁻¹ = 3 xy⁴ (Ans.)
8xy 8
Example.2) Divide 36a⁴b⁸c²d⁶ by 9a⁵bᶟc²d²
Ans.) As per the given condition, we have to 36a⁴b⁸c²d⁶ ÷ 9a⁵bᶟc²d²
36a⁴b⁸c²d⁶ ÷ 9a⁵bᶟc²d²
36a⁴b⁸c⁵d⁶ 36 a⁴ b⁸ c² d⁶
= ------------- = ------ X ------ X ------ X ------- X -------
9a⁵bᶟc²d² 9 a⁵ bᶟ c² d²
= 4 a⁴⁻⁵ b⁸⁻ᶟ c²⁻² d⁶⁻²
= 4 a⁻¹ b⁵ c⁰ d⁴ = 4 a⁻¹ b⁵ . 1 . d⁴
= 4 a⁻¹ b⁵ d⁴
4 b⁵ d⁴
= ------------ (Ans.)
a
Example.3) Divide 30x⁴y² + 15 x²y²- 20 x⁵y⁴ + 10 x⁵y⁶ - 25 x⁸y⁵ by 5 x⁴y⁶
Ans.) As per the given condition we have to 30x⁴y²+ 15 x²y²- 20 x⁵y⁴ + 10 x⁵y⁶ - 25 x⁸y⁵ ÷ 5 x⁴y⁶
30x⁴y²+ 15 x²y² - 20 x⁵y⁴ + 10 x⁵y⁶ - 25 x⁸y⁵ ÷ 5 x⁴y⁶
30x⁴y² + 15 x²y² - 20 x⁵y⁴ + 10 x⁵y⁶ - 25 x⁸y⁵
= ------------------------------------------------
5 x⁴y⁶
30x⁴y² 15 x²y² 20 x⁵y⁴ 10 x⁵y⁶ 25 x⁸y⁵
= --------- + --------- - ---------- + ---------- - -----------
5 x⁴y⁶ 5 x⁴y⁶ 5 x⁴y⁶ 5 x⁴y⁶ 5 x⁴y⁶
= 6 x⁴⁻⁴. y²⁻⁶ + 3 x²⁻⁴. y²⁻⁶ - 4 x⁵⁻⁴ y⁴⁻⁶ + 2 x⁵⁻⁴ y⁶⁻⁶ - 5 x⁸⁻⁴ y⁵⁻⁶
= 6 x⁰ y⁻⁴ + 3 x⁻² y⁻⁴ - 4 x¹ y⁻² + 2x¹ y⁰ - 5x⁴ y⁻¹
= 6.1. y⁻⁴ + 3 x⁻² y⁻⁴ - 4 x y⁻² + 2x.1 - 5x⁴ y⁻¹
= 6 y⁻⁴ + 3 x⁻² y⁻⁴ - 4 x y⁻² + 2x - 5x⁴ y⁻¹
6 3 4x 5x⁴
= -------- + -------- - --------- + 2x - --------- (Ans.)
y⁴ x² y⁴ y² y