Tính: \( ( - 0.5)^{{-4}} - 625^{0,25} - (2\dfrac{1}{4})^{-1\dfrac{1}{2}} \)
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Lời giải:
Báo sai\( ( - 0.5)^{{-4}} - 625^{0,25} - \Big(2\dfrac{1}{4}\Big)^{-1\dfrac{1}{2}} \)
\(=\Big( \dfrac{-1}{2}\Big)^{-4} - \Big( 5^{4}\Big)^{0,25} - \Big(\dfrac{9}{4}\Big)^{\dfrac{-3}{2}}\)
\(\begin{array}{l}
= \frac{1}{{{{\left( { - \frac{1}{2}} \right)}^4}}} - {5^{4.0,25}} - {\left( {{{\left( {\frac{3}{2}} \right)}^2}} \right)^{ - \frac{3}{2}}}\\
= \frac{1}{{\frac{1}{{16}}}} - {5^1} - {\left( {\frac{3}{2}} \right)^{2.\left( { - \frac{3}{2}} \right)}}
\end{array}\)
\(= 16 - 5 - \Big( \dfrac{3}{2}\Big)^{-3}\)
\(\begin{array}{l}
= 11 - \frac{1}{{{{\left( {\frac{3}{2}} \right)}^3}}}\\
= 11 - \frac{1}{{\frac{{27}}{8}}}
\end{array}\)
\(= 11 - \dfrac{8}{27} =\dfrac{289}{27}\)
