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Section 1.2 : Rational Exponents

7. Simplify the following expression and write the answer with only positive exponents.

\[{\left( {{a^3}\,{b^{ - \,\,\frac{1}{4}}}} \right)^{\frac{2}{3}}}\] 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.

\[{\left( {{a^3}\,{b^{ - \,\,\frac{1}{4}}}} \right)^{\frac{2}{3}}} = {a^2}\,{b^{ - \,\,\frac{1}{6}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{{a^2}}}{{{b^{\frac{1}{6}}}}}}}\]