Question

Bài 5: Tính:
1) \( \left( \frac{4}{7} \right)^2 \)
2) \( \left( -\frac{1}{2} \right)^3 \)
3) \( \left( \frac{1}{4} \right)^2 \)
4) \( \left( -\frac{1}{2} \right)^3 \)
5) \( \left( \frac{4}{7} \right)^2 \)
6) \( \left( \frac{1}{4} \right)^2 \)
7) \( \left( \frac{2}{3} \right)^2 \cdot \left( \frac{3}{4} \right)^3 \)
8) \( \frac{6}{18} \cdot \left( \frac{7}{3} \right)^2 \)
9) \( \frac{5^{12}}{6^{12}} \)
10) \( \left( \frac{1}{6} \right)^5 \cdot \left( \frac{1}{6} \right) \)
11) \( \left( -\frac{1}{2} \right)^5 \cdot \left( -\frac{1}{2} \right)^3 \)
12) \( \left( \frac{3}{7} \right)^4 \cdot \left( -\frac{3}{7} \right)^2 \)
13) \( \left( 2^3 \right)^4 \)
14) \( \left[ \left( \frac{2}{5} \right)^4 \right]^2 \)

Bài 6: Thực hiện phép tính (Tính lũy thừa)
1) \( \left( \frac{2}{3} \right)^2 \)
2) \( \left( \frac{2}{3} \right)^3 \)
3) \( \left( \frac{3}{5} \right)^0 \)
4) \( \left( \frac{3}{5} \right)^1 \)
5) \( \left( \frac{1}{2} \right)^2 \)
6) \( \left( -\frac{

Answer 1

Bài 5:

1: \(\left(\frac47\right)^2=\frac{4^2}{7^2}=\frac{16}{49}\)

2: \(\left(-\frac12\right)^3=\frac{\left(-1\right)^3}{2^3}=-\frac18\)

3: \(\left(1\frac14\right)^2=\left(\frac54\right)^2=\frac{25}{16}\)

4: \(\left(-\frac12\right)^3=\frac{\left(-1\right)^3}{2^3}=-\frac18\)

5: \(\left(\frac47\right)^2=\frac{4^2}{7^2}=\frac{16}{49}\)

6: \(\left(1\frac14\right)^2=\left(\frac54\right)^2=\frac{25}{16}\)

7: \(\left(\frac23\right)^3\cdot\left(\frac34\right)^3=\left(\frac23\cdot\frac34\right)^3=\left(\frac24\right)^3=\left(\frac12\right)^3=\frac18\)

8: \(\left(\frac{6}{18}\right)^2:\left(\frac73\right)^2=\left(\frac13\right)^2:\left(\frac73\right)^2=\left(\frac13:\frac73\right)^2=\left(\frac17\right)^2=\frac{1}{49}\)

9: \(\frac{5^{12}}{6^{12}}=\left(\frac56\right)^{12}\)

10: \(\left(\frac16\right)^5\cdot\left(\frac16\right)^2=\left(\frac16\right)^{5+2}=\left(\frac16\right)^7\)

11: \(\left(-\frac12\right)^5:\left(-\frac12\right)^3=\left(-\frac12\right)^{5-3}=\left(-\frac12\right)^2=\frac14\)

12: \(\left(\frac37\right)^4:\left(-\frac37\right)^2=\left(\frac37\right)^4:\left(\frac37\right)^2=\left(\frac37\right)^{4-2}=\left(\frac37\right)^2=\frac{9}{49}\)

13: \(\left(2^3\right)^4=2^{3\cdot4}=2^{12}=4096\)

14: \(\left\lbrack\left(\frac25\right)^4\right\rbrack^2=\left(\frac25\right)^{4\cdot2}=\left(\frac25\right)^8=\frac{256}{390625}\)

Bài 6:

1: \(\left(\frac32\right)^2=\frac{3^2}{2^2}=\frac94\)

2: \(\left(\frac23\right)^3=\frac{2^3}{3^3}=\frac{8}{27}\)

3: \(\left(-\frac13\right)^3=\frac{\left(-1\right)^3}{3^3}=-\frac{1}{27}\)

4: \(\left(-\frac25\right)^2=\frac{\left(-2\right)^2}{5^2}=\frac{4}{25}\)

5: \(\left(\frac{2}{-3}\right)^3=\frac{2^3}{\left(-3\right)^3}=-\frac{8}{27}\)

6: \(\left(-\frac34\right)^2=\frac{\left(-3\right)^2}{4^2}=\frac{9}{16}\)

7: \(\left(-\frac12\right)^1=-\frac12\)

8: \(\left(-\frac65\right)^2=\frac{\left(-6\right)^2}{5^2}=\frac{36}{25}\)

9: \(\left(-\frac{9}{21}\right)^0=1\)

10: \(\left(3\frac12\right)^2=\left(\frac72\right)^2=\frac{49}{4}\)

11: \(\left(2\frac15\right)^2=\left(\frac{11}{5}\right)^2=\frac{121}{25}\)

12: \(\left(-1\frac23\right)^2=\left(-\frac53\right)^2=\frac{25}{9}\)

13: \(\left(-1\frac12\right)^4=\left(-\frac32\right)^4=\frac{\left(-3\right)^4}{2^4}=\frac{81}{16}\)

14: \(\left(-1\frac25\right)^2=\left(-\frac75\right)^2=\frac{49}{25}\)

15: \(\left(-2\frac35\right)^2=\left(-\frac{13}{5}\right)^2=\frac{\left(-13\right)^2}{5^2}=\frac{169}{25}\)

16: \(\left(-1\frac34\right)^1=-1\frac34=-\frac74\)

17: \(\left(-9\frac{10}{11}\right)^0=1\)

18: \(\left(-2\frac14\right)^3=\left(-\frac94\right)^3=\frac{\left(-9\right)^3}{4^3}=-\frac{729}{64}\)

19: \(\left(-0,3\right)^3=\left(-\frac{3}{10}\right)^3=\frac{\left(-3\right)^3}{10^3}=-\frac{27}{1000}\)

20: \(\left(-1,1\right)^2=1,1^2=1,1\cdot1,1=1,21\)

21: \(\left(-1,2\right)^2=\left(-1,2\right)\cdot\left(-1.2\right)=1,2\cdot1,2=1,44\)

22: \(\left(-0,5\right)^2=0,5^2=0,5\cdot0,5=0,25\)

23: \(1,4^2=1,4\cdot1,4=1,96\)

24: \(0,8^3=0,8\cdot0,8\cdot0,8=0,512\)

25: \(0,25^3=\left(\frac14\right)^3=\frac{1^3}{4^3}=\frac{1}{64}\)

26: \(3,5^2=3,5\cdot3,5=12,25\)

27: \(\left(-0,987\right)^0=1\)

Bài 7:

1: \(\left(\frac83\right)^8\cdot\left(\frac94\right)^8=\left(\frac83\cdot\frac94\right)^8=\left(2\cdot3\right)^8=6^8\)

2: \(\left(\frac37\right)^{12}\cdot\left(\frac{21}{5}\right)^{12}=\left(\frac37\cdot\frac{21}{5}\right)^{12}=\left(3\cdot\frac35\right)^{12}=\left(\frac95\right)^{12}\)

3: \(\left(-\frac{4}{13}\right)^5\cdot\left(\frac{26}{5}\right)^5=\left(-\frac{4}{13}\cdot\frac{26}{5}\right)^5=\left(-4\cdot\frac25\right)^5=\left(-\frac85\right)^5\)

4: \(\left(\frac{12}{7}\right)^4\cdot\left(\frac{35}{16}\right)^4=\left(\frac{12}{7}\cdot\frac{35}{16}\right)^4=\left(\frac34\cdot5\right)^4=\left(\frac{15}{4}\right)^4\)

5: \(\left(\frac67\right)^{13}\cdot\left(\frac{49}{18}\right)^{13}=\left(\frac67\cdot\frac{49}{18}\right)^{13}=\left(\frac13\cdot7\right)^{13}=\left(\frac73\right)^{13}\)

6: \(\left(-\frac14\right)^{12}:\left(\frac{13}{12}\right)^{12}=\left(\frac14\right)^{12}:\left(\frac{13}{12}\right)^{12}=\left(\frac14:\frac{13}{12}\right)^{12}=\left(\frac{3}{13}\right)^{12}\)

7: \(\left(-\frac{10}{3}\right)^4:\left(-\frac56\right)^4=\left(\frac{10}{3}:\frac56\right)^4=\left(\frac{10}{3}\cdot\frac65\right)^4=\left(\frac{60}{15}\right)^4=4^4\)

8: \(\left(\frac47\right)^{19}:\left(-\frac{12}{35}\right)^{19}=\left(\frac47:\frac{-12}{35}\right)^{19}=\left(\frac47\cdot\frac{-35}{12}\right)^{19}=\left(-\frac53\right)^{19}\)

9: \(\left(-\frac47\right)^{11}:\left(-\frac{16}{28}\right)^{11}=\left(-\frac47\right)^{11}:\left(-\frac47\right)^{11}=1\)