1Cademy - Finding the Quotient $$\frac{14x^7y^{12}}{21x^{11}y^6}$$

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Dividing Monomials

Example

Finding the Quotient $\frac{14x^7y^{12}}{21x^{11}y^6}$

Divide two monomials in a single step by simultaneously reducing the coefficient and subtracting the exponents for each variable: $\frac{14x^7y^{12}}{21x^{11}y^6}$ .

Simplify the coefficient and apply the Quotient Property: The coefficients $14$ and $21$ share a common factor of $7$ : $\frac{14}{21} = \frac{2}{3}$ . For $x$ : since $11 > 7$ , the variable $x$ remains in the denominator with an exponent of $11 - 7 = 4$ . For $y$ : since $12 > 6$ , the variable $y$ remains in the numerator with an exponent of $12 - 6 = 6$ .

Putting all the pieces together gives $\frac{2y^6}{3x^4}$ .

The quotient is $\frac{2y^6}{3x^4}$ . Once familiar with the step-by-step process, monomial division can be executed in a single step by dividing out common factors from the coefficients and applying the Quotient Property to each variable.

Updated 2026-04-29

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