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Fractional Exponents

Simplify: (4a^{2}b^{3})^{\frac{1}{2}}(a^{6}b^{-\frac{3}{2}})^{\frac{1}{3}}.

 

Properties:

  • a^{\frac{m}{n}}=\sqrt[n]{a^m}
  • (a^{m})^{n}=a^{mn}
  • a^{-m}=\frac{1}{a^m}

(4a^{2}b^{3})^{\frac{1}{2}}(a^{6}b^{-\frac{3}{2}})^{\frac{1}{3}}

Distrubute:

=(4^{\frac{1}{2}})(a^{2})^{\frac{1}{2}}(b^{3})^{\frac{1}{2}}(a^{6})^{\frac{1}{3}}(b^{-\frac{3}{2}})^{\frac{1}{3}}

=(4^{\frac{1}{2}})(a^{1})(b^{\frac{3}{2}})(a^{2})(b^{-\frac{1}{2}})

=(\sqrt{4})(a^{3})(\sqrt{b^{3}})(\frac{1}{b^{\frac{1}{2}}})

=2(a^{3})(\sqrt{b^{3}})(\frac{1}{\sqrt{b}})

* \sqrt{b^{2}b}=b\sqrt{b}

=(2a^{3}b\sqrt{b})(\frac{1}{\sqrt{b}})

=2a^{3}b