Question

Calcule o valor das expressões
D)125^1/3 + 27^2/3 - 100^0

E)0,20^-6 x (1,5)^10

Answer 1

d)

$125^{\frac{1}{3}}~+~27^{\frac{1}{3}}~-~100^0~=\\\\\\=~\sqrt[3]{125}~+~\sqrt[3]{27}~-~1\\\\\\=~\sqrt[3]{5^3}~+~\sqrt[3]{3^3}~-~1\\\\\\=~\sqrt[3\!\!\!\backslash]{5^{3\!\!\!\backslash}}~+~\sqrt[3\!\!\!\backslash]{3^{3\!\!\!\backslash}}~-~1\\\\\\=~5~+~3~-~1\\\\\\=~\boxed{~7~}$

e)

$0,20^{-6}~\times~(1,5)^{10}~=\\\\\\=~\left(\frac{20}{100}\right)^{-6}~\times~\left(\frac{15}{10}\right)^{10}\\\\\\=~\left(\frac{1}{5}\right)^{-6}~\times~\left(\frac{3}{2}\right)^{10}\\\\\\=~\left(\frac{5}{1}\right)^{6}~\times~\frac{3^{10}}{2^{10}}\\\\\\=~\frac{5^6}{1^6}~\times~\frac{59049}{1024}\\\\\\=~\frac{15625}{1}~\times~\frac{59049}{1024}\\\\\\=~\boxed{\frac{922\,640\,625}{1\,024}}$