lam ho bai nay cho minh

Đáp án:

$\begin{array}{l}
40)\\
125 = {5^3}\\
 - 125 = {\left( { - 5} \right)^3}\\
27 = {3^3}\\
 - 27 = {\left( { - 3} \right)^3}\\
41)25 = {5^2} = {\left( { - 5} \right)^2}\\
42)a){\left( {x - \dfrac{1}{2}} \right)^2} = 0\\
 \Leftrightarrow x - \dfrac{1}{2} = 0\\
 \Leftrightarrow x = \dfrac{1}{2}\\
Vậy\,x = \dfrac{1}{2}\\
b){\left( {x - 2} \right)^2} = 1\\
 \Leftrightarrow \left[ \begin{array}{l}
x - 2 = 1\\
x - 2 =  - 1
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = 3\\
x = 1
\end{array} \right.\\
Vậy\,x = 1;x = 3\\
c){\left( {2x - 1} \right)^3} =  - 8\\
 \Leftrightarrow {\left( {2x - 1} \right)^3} = {\left( { - 2} \right)^3}\\
 \Leftrightarrow 2x - 1 =  - 2\\
 \Leftrightarrow 2x =  - 1\\
 \Leftrightarrow x =  - \dfrac{1}{2}\\
Vậy\,x =  - \dfrac{1}{2}\\
d){\left( {x + \dfrac{1}{2}} \right)^2} = \dfrac{1}{{16}}\\
 \Leftrightarrow \left[ \begin{array}{l}
x + \dfrac{1}{2} = \dfrac{1}{4}\\
x + \dfrac{1}{2} =  - \dfrac{1}{4}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{1}{4} - \dfrac{1}{2} =  - \dfrac{1}{4}\\
x =  - \dfrac{1}{4} - \dfrac{1}{2} =  - \dfrac{3}{4}
\end{array} \right.\\
Vậy\,x =  - \dfrac{1}{4};x =  - \dfrac{3}{4}\\
43){2^{225}} = {2^{3.75}} = {\left( {{2^3}} \right)^{75}} = {8^{75}}\\
{3^{150}} = {3^{2.75}} = {\left( {{3^2}} \right)^{75}} = {9^{75}}\\
Do:{8^{75}} < {9^{75}}\\
 \Leftrightarrow {2^{225}} < {3^{150}}
\end{array}$