QuestionAugust 26, 2025

4. 3b^(1)/(2)cdot b^(4)/(3)

4. 3b^(1)/(2)cdot b^(4)/(3)
4. 3b^(1)/(2)cdot b^(4)/(3)

Solution
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Answer

3b^{\frac{11}{6}} Explanation 1. Apply the Product of Powers Rule Use **a^m \cdot a^n = a^{m+n}** to combine the exponents: b^{\frac{1}{2}} \cdot b^{\frac{4}{3}} = b^{\frac{1}{2} + \frac{4}{3}}. 2. Simplify the Exponent Convert \frac{1}{2} and \frac{4}{3} to a common denominator: \frac{1}{2} = \frac{3}{6}, \frac{4}{3} = \frac{8}{6}. Add them: \frac{3}{6} + \frac{8}{6} = \frac{11}{6}. 3. Combine with Coefficient Multiply by 3: 3b^{\frac{11}{6}}.

Explanation

1. Apply the Product of Powers Rule<br /> Use **$a^m \cdot a^n = a^{m+n}$** to combine the exponents: $b^{\frac{1}{2}} \cdot b^{\frac{4}{3}} = b^{\frac{1}{2} + \frac{4}{3}}$.<br />2. Simplify the Exponent<br /> Convert $\frac{1}{2}$ and $\frac{4}{3}$ to a common denominator: $\frac{1}{2} = \frac{3}{6}$, $\frac{4}{3} = \frac{8}{6}$. Add them: $\frac{3}{6} + \frac{8}{6} = \frac{11}{6}$.<br />3. Combine with Coefficient<br /> Multiply by 3: $3b^{\frac{11}{6}}$.
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