Bài 3: Thực hiện phép tính

1) \( 12 \left( \frac{1}{3} \right)^2 + \frac{2}{3} \)

2) \( 18 \left( \frac{1}{2} \right)^2 + \frac{5}{2} \)

3) \( 15 \left( -\frac{2}{3} \right)^2 - \frac{7}{3} \)

4) \( \left( \frac{1}{3} \right)^2 \cdot 3 - \frac{2}{9} \cdot \frac{2}{3} \)

5) \( \left( \frac{1}{3} \right)^3 \cdot \frac{9}{4} - \left( -\frac{1}{2} \right)^2 \)

6) \( \left( -\frac{3}{2} \right)^2 - \left( -\frac{1}{2} \right) \cdot 6 \)

7) \( 3 \left( -\frac{3}{2} \right)^2 + \frac{1}{9} \cdot 6^4 \)

Bây giờ, chúng ta sẽ thực hiện từng phép tính một:

1) \( 12 \left( \frac{1}{3} \right)^2 + \frac{2}{3} = 12 \cdot \frac{1}{9} + \frac{2}{3} = \frac{12}{9} + \frac{2}{3} = \frac{4}{3} + \frac{2}{3} = 2 \)

2) \( 18 \left( \frac{1}{2} \right)^2 + \frac{5}{2} = 18 \cdot \frac{1}{4} + \frac{5}{2} = \frac{18}{4} + \frac{5}{2} = \frac{9}{2} + \frac{5}{2} = 7 \)

3) \( 15 \left( -\frac{2}{3} \right)^2 - \frac{7}{3} = 15 \cdot \frac{4}{9} - \frac{7}{3} = \frac{60}{9} - \frac{7}{3} = \frac{20}{3} - \frac{7}{3} = \frac{13}{3} \approx 4.33 \)

4) \( \left( \frac{1}{3} \right)^2 \cdot 3 - \frac{2}{9} \cdot \frac{2}{3} = \frac{1}{9} \cdot 3 - \frac{4}{27} = \frac{3}{9} - \frac{4}{27} = \frac{9}{27} - \frac{4}{27} = \frac{5}{27} \approx 0.185 \)

5) \( \left( \frac{1}{3} \right)^3 \cdot \frac{9}{4} - \left( -\frac{1}{2} \right)^2 = \frac{1}{27} \cdot \frac{9}{4} - \frac{1}{4} = \frac{9}{108} - \frac{1}{4} = \frac{1}{12} - \frac{1}{4} = \frac{1}{12} - \frac{3}{12} = -\frac{2}{12} = -\frac{1}{6} \approx -0.167 \)

6) \( \left( -\frac{3}{2} \right)^2 - \left( -\frac{1}{2} \right) \cdot 6 = \frac{9}{4} + 3 = \frac{9}{4} + \frac{12}{4} = \frac{21}{4} = 5.25 \)

7) \( 3 \left( -\frac{3}{2} \right)^2 + \frac{1}{9} \cdot 6^4 = 3 \cdot \frac{9}{4} + \frac{1}{9} \cdot 1296 = \frac{27}{4} + 144 = 6.75 + 144 = 150.75 \)

Vậy kết quả của các phép tính là:

1) 2
2) 7
3) \(\frac{13}{3} \approx 4.33\)
4) \(\frac{5}{27} \approx 0.185\)
5) \(-\frac{1}{6} \approx -0.167\)
6) 5.25
7) 150.75