QuestionAugust 27, 2025

Simplify (-6a^3b^-1)/(36ab^2) -6a^2b^3 -(a^2)/(6b^3) -(a^2b^3)/(6) -(6a^2)/(b^3)

Simplify (-6a^3b^-1)/(36ab^2) -6a^2b^3 -(a^2)/(6b^3) -(a^2b^3)/(6) -(6a^2)/(b^3)
Simplify (-6a^3b^-1)/(36ab^2) -6a^2b^3 -(a^2)/(6b^3) -(a^2b^3)/(6) -(6a^2)/(b^3)

Solution
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Answer

-\frac{a^{2}}{6b^{3}} Explanation 1. Simplify the coefficients Divide the coefficients: \frac{-6}{36} = -\frac{1}{6}. 2. Simplify the powers of a Use **a^{m}/a^{n} = a^{m-n}**: a^{3-1} = a^{2}. 3. Simplify the powers of b Use **b^{m}/b^{n} = b^{m-n}**: b^{-1-2} = b^{-3}. 4. Combine the simplified terms Combine results: -\frac{1}{6} \cdot a^{2} \cdot b^{-3} = -\frac{a^{2}}{6b^{3}}.

Explanation

1. Simplify the coefficients<br /> Divide the coefficients: $\frac{-6}{36} = -\frac{1}{6}$.<br />2. Simplify the powers of $a$<br /> Use **$a^{m}/a^{n} = a^{m-n}$**: $a^{3-1} = a^{2}$.<br />3. Simplify the powers of $b$<br /> Use **$b^{m}/b^{n} = b^{m-n}$**: $b^{-1-2} = b^{-3}$.<br />4. Combine the simplified terms<br /> Combine results: $-\frac{1}{6} \cdot a^{2} \cdot b^{-3} = -\frac{a^{2}}{6b^{3}}$.
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