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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 Solution

There isn’t really a lot to do here other than to use the exponent properties from the previous section to do the simplification.

${\left( {\frac{{{q^3}\,{p^{ - \frac{1}{2}}}}}{{{q^{ - \frac{1}{3}}}\,p}}} \right)^{\frac{3}{7}}} = {\left( {\frac{{{q^3}\,{q^{\frac{1}{3}}}}}{{\,p{p^{\frac{1}{2}}}}}} \right)^{\frac{3}{7}}}\, = {\left( {\frac{{{q^{\frac{{10}}{3}}}}}{{\,{p^{\frac{3}{2}}}}}} \right)^{\frac{3}{7}}}\, = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{{q^{\frac{{10}}{7}}}}}{{\,{p^{\frac{9}{{14}}}}}}}}$