1Cademy - Finding the Quotient $$54a^2b^3 \div (-6ab^5)$$

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Dividing Monomials

Example

Finding the Quotient $54a^2b^3 \div (-6ab^5)$

Divide two monomials that contain multiple variables and a negative denominator: $54a^2b^3 \div (-6ab^5)$ .

Step 1 — Rewrite as a fraction. $\frac{54a^2b^3}{-6ab^5}$

Step 2 — Separate using fraction multiplication. Break the fraction into three parts — one for the coefficients and one for each variable: $\frac{54}{-6} \cdot \frac{a^2}{a} \cdot \frac{b^3}{b^5}$

Step 3 — Simplify and use the Quotient Property. For the coefficients: $\frac{54}{-6} = -9$ . For $a$ : $\frac{a^2}{a} = a$ . For $b$ : $\frac{b^3}{b^5} = \frac{1}{b^2}$ . Combining these gives: $-9 \cdot a \cdot \frac{1}{b^2}$ .

Step 4 — Multiply. $-\frac{9a}{b^2}$

The quotient is $-\frac{9a}{b^2}$ .

Updated 2026-04-29

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OpenStax Intermediate Algebra

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