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### Section 1.2 : Rational Exponents

For problems 1 – 6 evaluate the given expression and write the answer as a single number with no exponents.

1. $${36^{\frac{1}{2}}}$$ Solution
2. $${\left( { - 125} \right)^{\frac{1}{3}}}$$ Solution
3. $$- {16^{\frac{3}{2}}}$$ Solution
4. $${27^{ -\frac{5}{3}}}$$ Solution
5. $$\left( {\frac{9}{4}} \right)^{\frac{1}{2}}$$ Solution
6. $$\left( {\frac{8}{{343}}} \right)^{ - \frac{2}{3}}$$ Solution

For problems 7 – 10 simplify the given expression and write the answer with only positive exponents.

1. $${\left( {{a^3}\,{b^{ - \frac{1}{4}}}} \right)^{\frac{2}{3}}}$$ Solution
2. $${x^{\frac{1}{4}}}\,{x^{ - \frac{1}{5}}}$$ Solution
3. $$\left( {\frac{{{q^3}\,{p^{ - \frac{1}{2}}}}}{{{q^{ - \frac{1}{3}}}\,p}}} \right)^{\frac{3}{7}}$$ Solution
4. $$\left( {\frac{{{m^{\frac{1}{2}}}\,{n^{ - \frac{1}{3}}}}}{{{n^{\frac{2}{3}}}\,{m^{ - \frac{7}{4}}}}}} \right)^{ - \frac{1}{6}}$$ Solution