Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
a,\\
{\left( { - 1\dfrac{1}{4}} \right)^2} = {\left( {\dfrac{{ - 5}}{4}} \right)^2} = {\left( {\dfrac{5}{4}} \right)^2} = \dfrac{{25}}{{16}}\\
b,\\
{45^{10}}{.5^{20}} = {\left( {{{5.3}^2}} \right)^{10}}{.5^{20}} = {5^{10}}.{\left( {{3^2}} \right)^{10}}{.5^{20}} = {5^{10}}{.3^{20}}{.5^{20}} = {5^{30}}{.3^{20}}\\
c,\\
3 - {\left( { - \dfrac{6}{7}} \right)^0} + {\left( {\dfrac{1}{2}} \right)^2}:{2^2} = 3 - 1 + \dfrac{1}{4}:4 = 2 + \dfrac{1}{{16}} = \dfrac{{33}}{{16}}\\
2,\\
a,\\
\left| {x + \dfrac{4}{5}} \right| - \dfrac{1}{2} = 0\\
\Leftrightarrow \left| {x + \dfrac{4}{5}} \right| = \dfrac{1}{2}\\
\Leftrightarrow \left[ \begin{array}{l}
x + \dfrac{4}{5} = \dfrac{1}{2}\\
x + \dfrac{4}{5} = - \dfrac{1}{2}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{1}{2} - \dfrac{4}{5}\\
x = - \dfrac{1}{2} - \dfrac{4}{5}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = - \dfrac{3}{{10}}\\
x = \dfrac{{ - 13}}{{10}}
\end{array} \right.\\
b,\\
{\left( {2x - 1} \right)^3} - 7 = 20\\
\Leftrightarrow {\left( {2x - 1} \right)^3} = 27\\
\Leftrightarrow {\left( {2x - 1} \right)^3} = {3^3}\\
\Leftrightarrow 2x - 1 = 3\\
\Leftrightarrow 2x = 4\\
\Leftrightarrow x = 2
\end{array}\)
