Uprostiti sledeći izraz:

${243}^{\frac{1}{5}}-{\left(\frac{1}{81}\right)}^{\frac{1}{4}}+{\left(64+7,5\right)}^{0}+{\left({9}^{\frac{7}{8}}:{3}^{\frac{5}{4}}\right)}^{4}$

${243}^{\frac{1}{5}}-{\left(\frac{1}{81}\right)}^{\frac{1}{4}}+{\left(92+7,5\right)}^{0}+{\left({9}^{\frac{7}{8}}:{3}^{\frac{5}{4}}\right)}^{4}$

${243}^{\frac{1}{5}}-{\left(\frac{1}{81}\right)}^{\frac{1}{4}}+{\left(92+7,5\right)}^{0}+{\left({9}^{\frac{7}{8}}:{3}^{\frac{5}{4}}\right)}^{4}$

$={\left({3}^{5}\right)}^{\frac{1}{5}}-{\left(\frac{1}{{3}^{4}}\right)}^{\frac{1}{4}}+{\left(92+7,5\right)}^{0}+{\left[{\left({3}^{2}\right)}^{\frac{7}{8}}:{3}^{\frac{5}{4}}\right]}^{4}$

$={3}^{\frac{5}{5}}-\frac{{1}^{\frac{1}{4}}}{{3}^{\frac{4}{4}}}+1+{\left({3}^{\frac{14}{8}}·{3}^{-\frac{5}{4}}\right)}^{4}$

$=3-\frac{1}{3}+1+{\left[{3}^{\frac{14}{8}-\frac{5}{4}}\right]}^{4}$

$=3-\frac{1}{3}+1+{\left({3}^{\frac{14-2·5}{8}}\right)}^{4}$

$=4-\frac{1}{3}+{\left({3}^{\frac{4}{8}}\right)}^{4}$

$=3-\frac{1}{3}+1+{3}^{\frac{16}{8}}$

$=3-\frac{1}{3}+1+{3}^{2}$
$=3-\frac{1}{3}+1+9$
$=\frac{9-1+3+27}{3}$

$=\frac{38}{3}$