Question

256 la puterea 4/5 ori 1 pe 64 la puterea 2/3 ( doar 64 este ridicat la puterea 2/3

Answer 1

$256^{\frac{4}{5}}\cdot\frac{1}{64^{\frac{2}{3}}}=$
$\frac{256^{\frac{4}{5}}}{64^{\frac{2}{3}}}=$
$\frac{(2^8)^{\frac{4}{5}}}{(2^6)^{\frac{2}{3}}}=$
$\frac{2^{\frac{32}{5}}}{2^{\frac{12}{3}}}=$
$\frac{2^{\frac{32}{5}}}{2^4}=$
$2^{\frac{32}{5}-4}=$
$2^{\frac{32}{5}-\frac{20}{5}}=$
$2^{\frac{12}{5}}=2^{2,4}$