Question

Preciso muito de ajuda nas questões da foto..

Answer 1

$a) \ 3^0=1\\ \\ b) \ (-5)^1=-5\\ \\ c) \ (-1)^{20}=1\\ \\ d) \ 5^{-1}=\frac{1}{5}\\ \\ e) \ (\frac{3}{2})^{-3}=(\frac{2}{3})^3=\frac{8}{27}\\ \\ f) \ 9^{0,5}=9^{\frac{1}{2}}=\sqrt{9}=3\\ \\ g) \ 32^{-0,2}=(\frac{1}{32})^{\frac{1}{5}}= \sqrt[5]{\frac{1}{32}}=\frac{1}{2}$

$h) \ 8^{0,666...}=8^{\frac{1}{3}}= \sqrt[3]{8} =2\\ \\ i) \ (\frac{1}{9})^{-\frac{3}{2}}=9^{\frac{3}{2}}= \sqrt{9^3}= \sqrt{729}\\ \\ j) ( \sqrt{2} )^{-\frac{2}{3}}=(\frac{ \sqrt{2} }{2})^{\frac{2}{3}}= \sqrt[3]{\frac{1}{2}} \\ \\ k) \ (\frac{8}{27})^{-\frac{4}{3}}=(\frac{27}{8})^{\frac{4}{3}}= \sqrt[3]{(\frac{27}{8})^4}\\ \\ l) \ (0,333...)^{-\frac{1}{2}}=(\frac{1}{3})^{-\frac{1}{2}}}=3^{\frac{1}{2}}= \sqrt{3}$