So sánh: a) (− 2)^4 . (− 2)^5 và (− 2)^12 : (− 2)^3; b) (1/2)^2. (1/6)^6 và [(1/2)^4]^2

* Hướng dẫn giải

a) Ta có: (− 2)⁴ . (− 2)⁵ = (− 2)^{4 + 5} = (− 2)⁹;

(− 2)¹² : (− 2)³ = (− 2)^{12 – 3} = (− 2)⁹.

Ta thấy: (− 2)⁴ . (− 2)⁵ = (− 2)⁹ = (− 2)¹² : (− 2)³.

Vậy (− 2)⁴ . (− 2)⁵ = (− 2)¹² : (− 2)³.

b) Ta có:

$$\begin{gathered} {\left(\frac{1}{2}\right)}^2.{\left(\frac{1}{2}\right)}^6={\left(\frac{1}{2}\right)}^{2+6}={\left(\frac{1}{2}\right)}^8 \\ {\left[{\left(\frac{1}{2}\right)}^4\right]}^2={\left(\frac{1}{2}\right)}^{4.2}={\left(\frac{1}{2}\right)}^8 \\ Ta thấy {\left(\frac{{\displaystyle 1}}{{\displaystyle 2}}\right)}^2.{\left(\frac{{\displaystyle 1}}{{\displaystyle 2}}\right)}^6={\left(\frac{{\displaystyle 1}}{{\displaystyle 2}}\right)}^8={\left[{\left(\frac{{\displaystyle 1}}{{\displaystyle 2}}\right)}^4\right]}^2 \\ Vậy {\left(\frac{{\displaystyle 1}}{{\displaystyle 2}}\right)}^2.{\left(\frac{{\displaystyle 1}}{{\displaystyle 2}}\right)}^6={\left[{\left(\frac{{\displaystyle 1}}{{\displaystyle 2}}\right)}^4\right]}^2 \end{gathered}$$

c)