Section 1.2 : Rational Exponents
For problems 1 – 6 evaluate the given expression and write the answer as a single number with no exponents.
- \({36^{\frac{1}{2}}}\) Solution
- \({\left( { - 125} \right)^{\frac{1}{3}}}\) Solution
- \( - {16^{\frac{3}{2}}}\) Solution
- \({27^{ -\frac{5}{3}}}\) Solution
- \({\displaystyle \left( {\frac{9}{4}} \right)^{\frac{1}{2}}}\) Solution
- \({\displaystyle \left( {\frac{8}{{343}}} \right)^{ - \frac{2}{3}}}\) Solution
For problems 7 – 10 simplify the given expression and write the answer with only positive exponents.
- \({\left( {{a^3}\,{b^{ - \frac{1}{4}}}} \right)^{\frac{2}{3}}}\) Solution
- \({x^{\frac{1}{4}}}\,{x^{ - \frac{1}{5}}}\) Solution
- \({\displaystyle \left( {\frac{{{q^3}\,{p^{ - \frac{1}{2}}}}}{{{q^{ - \frac{1}{3}}}\,p}}} \right)^{\frac{3}{7}}}\) Solution
- \({\displaystyle \left( {\frac{{{m^{\frac{1}{2}}}\,{n^{ - \frac{1}{3}}}}}{{{n^{\frac{2}{3}}}\,{m^{ - \frac{7}{4}}}}}} \right)^{ - \frac{1}{6}}}\) Solution