Solution assignment 10 Rules for exponents

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Opgave 10

Simplify:

$\displaystyle\frac{{\sqrt[7]{{\frac{{a^2 b^{\frac{2}{3}} c^3 }}{{ab^2 \sqrt a }}}}}}{{a^2 b^3 c}}$

Solution

First work out the expression under the root sign and next write the root as an exponential function:

$\displaystyle\frac{{\sqrt[7]{{\frac{{a^2 b^{\frac{2}{3}} c^3 }}{{ab^2 \sqrt a }}}}}}{{a^2 b^3 c}} =\displaystyle\frac{{\sqrt[7]{{\frac{{a^{\frac{1}{2}} c^3 }}{{b^{\frac{4}{3}} }}}}}}{{a^2 b^3 c}} =\displaystyle\frac{{a^{\frac{1}{{14}}} c^{\frac{3}{7}} b^{ - \frac{4}{{21}}} }}{{a^2 b^3 c}} = a^{ - \frac{27}{14}}b^{ - \frac{{67}}{21}} c^{ - \frac{{4}}{{7}}}$

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Solution assignment 10 Rules for exponents

Opgave 10

Solution

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