Simplify $ \sqrt{a^{3} b^{4}} \cdot \sqrt[3]{a^{4} b^{3}} $.

Given:

\( \sqrt{a^{3} b^{4}} \cdot \sqrt[3]{a^{4} b^{3}} \).

To do:

We have to simplify \( \sqrt{a^{3} b^{4}} \cdot \sqrt[3]{a^{4} b^{3}} \).

Solution:

We know that,

$a^m \times a^n=a^{m+n}$

Therefore,

$\sqrt{a^{3} b^{4}} \cdot \sqrt[3]{a^{4} b^{3}}=a^{\frac{3}{2}}b^{\frac{4}{2}} \cdot a^{\frac{4}{3}}b^{\frac{3}{3}}$

$=a^{\frac{3}{2}}b^1 \cdot a^{\frac{4}{3}}b^1$

$=a^{\frac{3}{2}+\frac{4}{3}} \cdot b^{1+1}$

$=a^{\frac{3\times3+2\times4}{6}}b^2$

$=a^{\frac{17}{6}}b^2$
Hence,  $\sqrt{a^{3} b^{4}} \cdot \sqrt[3]{a^{4} b^{3}}=a^{\frac{17}{6}}b^2$.

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Updated on: 10-Oct-2022

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