Soluciones: Operaciones con exponentes fraccionarios o negativos

A continuación se presentan las soluciones de los ejercicios propuestos para practicar operaciones con exponentes fraccionarios o negativos en expresiones algebraicas:

761.

$\large \frac{cb^{2}}{a^{-4}\, b^{3}c^{2}d^{2}}=\frac{a^{4}}{bcd^{2}}$

762.

$\large 16a^{-5}\, b^{-7}=\frac{15}{a^{5}b^{7}}$

763.

$\large \frac{24a^{3}b^{2}}{a^{3}b^{4}}=\frac{24}{ab^{2}}$

764.

$\large 15a^{-\frac{13}{5}}\, b^{2}c^{\frac{3}{2}}$

765.

$\large -8a^{\frac{7}{6}}\, b^{\frac{5}{4}}\, c^{\frac{19}{20}}$

766.

$\large a^{\frac{101}{60}}$

767.

$\large b^{\frac{7}{4}}$

768.

$\large \sqrt[5]{a^{3}}.\sqrt[3]{a^{2}}=\sqrt[15]{a^{9}}.\sqrt[15]{a^{10}}=\sqrt[15]{a^{19}}=a^{\frac{19}{15}}$

769.

$\large a^{-\frac{3}{4}+\frac{5}{6}}=a^{\frac{1}{12}}$

770.

$\large \sqrt[4]{a^{\frac{1}{27}}\, .\, a^{\frac{5}{6}}}=\sqrt[4]{a^{\frac{141}{162}}}=a^{\frac{141}{648}}$

771.

$\large 4a^{\frac{1}{3}}\, b^{\frac{1}{2}}\, c^{\frac{5}{4}}$

772.

$\large 3a^{\frac{3}{2}}\, b^{\frac{1}{3}}-2a^{\frac{1}{2}}\, b+6a^{\frac{5}{2}}\, b^{\frac{3}{2}}$

773.

$\large a^{\frac{1}{3}}$

774.

$\large a$

775.

$\large a^{\frac{1}{6}}$

776.

$\large 25a^{4}\, b^{\frac{3}{4}}\, c$

777.

$\large -ab^{\frac{3}{8}}\, c^{3}$

778.

$\large a^{-\frac{1}{12}}$

779.

$\large a^{\frac{3}{4}}+2a^{\frac{8}{3}}\, b^{\frac{1}{4}}+a^{4}b^{\frac{1}{2}}$

780.

$\large a^{\frac{11}{4}}\, b^{\frac{1}{6}}\, c^{-\frac{2}{5}}$

781.

$\large 5a^{\frac{1}{3}}\, b^{\frac{1}{8}}\, c^{\frac{3}{10}}$

782.

$\large -2a^{\frac{2}{9}}\, b^{\frac{1}{12}}\, c^{\frac{2}{15}}$

783.

$\large 6a^{\frac{1}{5}}\, b^{\frac{7}{6}}\, c^{2}$

784.

$\large a^{\frac{3}{4}-\frac{4}{5}}=a^{-\frac{1}{20}}=a^{\frac{1}{\frac{1}{20}}}=a^{20}$

785.

$\large a^{\frac{9}{10}}\, b^{-\frac{1}{8}}=\sqrt[10]{a^{9}}.\, \sqrt[\frac{1}{8}]{b}$

786.

$\large a^{\frac{15}{4}}$

787.

$\large b^{-10}=\frac{1}{b^{10}}$

788.

$\large 64a^{-3}\, b^{\frac{9}{2}}=64.\frac{1}{a^{3}}.\sqrt{9}$

789.

$\large a$

790.

$\large a^{\frac{2}{9}}=\sqrt[9]{a^{2}}$

791.

$\large b^{-\frac{3}{8}}=\frac{1}{b^{\frac{3}{8}}}=\frac{1}{\sqrt[8]{b^{3}}}$

792.

$\large a^{\frac{1}{5}}\, b^{-\frac{2}{3}}=\sqrt[5]{a}\, .\, \frac{1}{b^{\frac{2}{3}}}=\sqrt[5]{a}\, .\, \frac{1}{\sqrt[3]{b^{2}}}$

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