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Section 1.2 : Rational Exponents
9. Simplify the following expression and write the answer with only positive exponents.
\[{\left( {\frac{{{q^3}\,{p^{ - \frac{1}{2}}}}}{{{q^{ - \frac{1}{3}}}\,p}}} \right)^{\frac{3}{7}}}\] Show SolutionThere isn’t really a lot to do here other than to use the exponent properties from the previous section to do the simplification.
\[{\left( {\frac{{{q^3}\,{p^{ - \frac{1}{2}}}}}{{{q^{ - \frac{1}{3}}}\,p}}} \right)^{\frac{3}{7}}} = {\left( {\frac{{{q^3}\,{q^{\frac{1}{3}}}}}{{\,p{p^{\frac{1}{2}}}}}} \right)^{\frac{3}{7}}}\, = {\left( {\frac{{{q^{\frac{{10}}{3}}}}}{{\,{p^{\frac{3}{2}}}}}} \right)^{\frac{3}{7}}}\, = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{{q^{\frac{{10}}{7}}}}}{{\,{p^{\frac{9}{{14}}}}}}}}\]