Question

Вычислите:
$16^{frac{1}{2} } + 27^{-frac{1}{3} } + 81^{frac{3}{4} }-8^{1frac{2}{3} }$

Answer 1

$16^{frac{1}{2}}=(4^2)^{frac{1}{2}}=4^{2*frac{1}{2}}=4^1=4;$

$27^{-frac{1}{3}}=(3^3)^{-frac{1}{3}}=3^{3*(-frac{1}{3})}=\\3^{-1}=frac{1}{3^1}=frac{1}{3};$

$81^{frac{3}{4}}=(3^4)^{frac{3}{4}}=3^{4*frac{3}{4}}=3^3=27;$

$8^{1frac{2}{3}}=(2^3)^{frac{1*3+2}{3}}=2^{3*frac{5}{3}}=2^{5}=32;$

$16^{frac{1}{2}}+27^{-frac{1}{3}}+81^{frac{3}{4}}-8^{1frac{2}{3}}=\\4+frac{1}{3}+27-32=-frac{2}{3}$