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Solution assignment 09 Rules for exponents

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Assignment 9

Simplify:

\displaystyle\frac{{a^2 b^{ - \frac{1}{2}} \sqrt c }}{{a^{\frac{1}{2}} b^{ - \frac{3}{2}} c}}

Solution

First change the root into a broken exponent:

\displaystyle\frac{{a^2 b^{ - \frac{1}{2}} \sqrt c }}{{a^{\frac{1}{2}} b^{ - \frac{3}{2}} c}} = \displaystyle\frac{{a^2 b^{ - \frac{1}{2}} c^{\frac{1}{2}} }}{{a^{\frac{1}{2}} b^{ - \frac{3}{2}} c}} = a^{\frac{3}{2}} bc^{ - \frac{1}{2}} =\displaystyle \frac{{ab \sqrt a }}{{\sqrt c }}

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