Zjednodušení výrazu
Zjednoduš následující výrazy pro a > 0 a b > 0:
\large {{{b^{ \Large \frac{2}{3}\large }}}} : {{{b^{ - \Large \frac{1}{3}\large }}}}
\large \Large \frac{{{b^{ \frac{2}{3}}}}}{{{b^{ - \frac{1}{3}}}}}\large = {b^{\left[ {\Large \frac{2}{3}\large -\left( { - \Large \frac{1}{3}\large } \right) } \right] }} = {b^{\left( {\Large \frac{2}{3}\large -\Large \frac{1}{3}\large } \right) }} = {b^{\frac{1}{3}}}
\large \Large \frac{{{b^{ \frac{2}{3}}}}}{{{b^{ - \frac{1}{3}}}}}\large = {b^{\left[ {\Large \frac{2}{3}\large -\left( { - \Large \frac{1}{3}\large } \right) } \right] }} = {b^{\left( {\Large \frac{2}{3}\large +\Large \frac{1}{3}\large } \right) }} = {b^{1}} = b
\large \Large \frac{{{b^{ \frac{2}{3}}}}}{{{b^{ - \frac{1}{3}}}}}\large = {b^{\left[ {\Large \frac{2}{3}\large -\left( { - \Large \frac{1}{3}\large } \right) } \right] }} = {b^{\left( {\Large \frac{2}{3}\large +\Large \frac{1}{3}\large } \right) }} = {b^{0}}
\large \Large \frac{{{b^{ \frac{2}{3}}}}}{{{b^{ - \frac{1}{3}}}}}\large = {b^{\left[ {\Large \frac{2}{3}\large -\left( { - \Large \frac{1}{3}\large } \right) } \right] }} = {b^{\left( {\Large \frac{2}{3}\large +\Large \frac{1}{3}\large } \right) }} = {b^{2}}
Máš tu opět dělení, budeš tedy odečítat exponent dělitele od exponentu dělence. Pozor, odečítáš záporný zlomek, takže jej vlastně přičítáš.
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