Tính :
a) \(\left(\dfrac{1}{16}\right)^{-\dfrac{3}{4}}+810000^{0,25}-\left(7\dfrac{19}{32}\right)^{\dfrac{1}{5}}\)
b) \(\left(0,001\right)^{-\dfrac{1}{3}}-2^{-2}.64^{\dfrac{2}{3}}-8^{-1\dfrac{1}{3}}\)
c) \(27^{\dfrac{2}{3}}-\left(-2\right)^{-2}+\left(3\dfrac{3}{8}\right)^{-\dfrac{1}{3}}\)
d) \(\left(-0,5\right)^{-4}-625^{0,25}-\left(2\dfrac{1}{4}\right)^{-1\dfrac{1}{2}}\)
a) \(\left(\dfrac{1}{16}\right)^{-\dfrac{3}{4}}+810000^{0.25}-\left(7\dfrac{19}{32}\right)^{\dfrac{1}{5}}\)
\(=\left(\dfrac{1}{2}\right)^{4.\left(-\dfrac{3}{4}\right)}+\left(30\right)^{4.0,25}-\left(\dfrac{243}{32}\right)^{\dfrac{1}{5}}\)
\(=\left(\dfrac{1}{2}\right)^{-3}+30-\left(\dfrac{3}{2}\right)^{5.\dfrac{1}{5}}\)
\(=2^3+30-\dfrac{3}{2}\)
\(=36,5\)
b) \(=\left(0,1\right)^{3.\left(-\dfrac{1}{3}\right)}-2^{-2}.2^{6.\dfrac{2}{3}}-\left[\left(2\right)^3\right]^{-\dfrac{4}{3}}\)
\(=0,1^{-1}-2^2-2^{-4}\)
\(=10-4-\dfrac{1}{16}\)
\(=\dfrac{95}{16}\)
c) \(=3^{3.\dfrac{2}{3}}-\dfrac{1}{\left(-2\right)^2}+\left(\dfrac{27}{8}\right)^{-\dfrac{1}{3}}\)
\(=9-\dfrac{1}{4}+\left(\dfrac{3}{2}\right)^{3.\dfrac{-1}{3}}\)
\(=9-\dfrac{1}{4}+\left(\dfrac{3}{2}\right)^{-1}\)
\(=9-\dfrac{1}{4}+\dfrac{2}{3}\)
\(=\dfrac{113}{12}\)
d) \(=\left(-\dfrac{1}{2}\right)^{-4}-5^{4.0,25}-\left(\dfrac{9}{4}\right)^{-\dfrac{3}{2}}\)
\(=\left(-2\right)^4-5-\left(\dfrac{3}{2}\right)^{2.\dfrac{-3}{2}}\)
\(=16-5-\left(\dfrac{3}{2}\right)^{-3}\)
\(=11-\dfrac{8}{27}\)
\(=\dfrac{289}{27}\)
