Question

(UEL-PR) Simplificando a expressão (0,0016)^-3/4 + (0,04)^-0,5 - 9 x (0,216)^-2/3

Answer 1

$(0,0016)^{-\frac{3}{4}} + (0,04)^{-0,5} - 9 \cdot (0,216)^{-\frac{2}{3}}= \\ \\ =(0,0001\cdot16)^{-\frac{3}{4}} + (0,01\cdot4)^{-\frac{1}{2}} - 9 \cdot (0,1\cdot216)^{-\frac{2}{3}}= \\ \\ =(10^{-4}\cdot16)^{-\frac{3}{4}} + (10^{-2}\cdot4)^{-\frac{1}{2}} - 9 \cdot (10^{-1}\cdot216)^{-\frac{2}{3}}= \\ \\ =10^{3}\cdot(\sqrt[4]{16})^{-3} + 10\cdot(\sqrt{4})^{-1}- 9 \cdot [10^{\frac{2}{3}}\cdot(\sqrt[3]{216})^{-2}]=$

$=10^{3}\cdot2^{-3} + 10\cdot2^{-1}- 9 \cdot [10^{\frac{2}{3}}\cdot6^{-2}]= \\ \\ =10^{3}\cdot\frac{1}{8} + 10\cdot\frac{1}{2}- 10^{\frac{2}{3}}\cdot\frac{9}{36}= \\ \\ =10^{3}\cdot\frac{1}{8} + 10\cdot\frac{1}{2}- 10^{\frac{2}{3}}\cdot\frac{1}{4}= \\ \\ =125+5-\frac{\sqrt[3]{100}}{4}=\\ \\ =\frac{520-\sqrt[3]{100}}{4}$