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1. 53 = 5.5.5 = 125
2. 27 = 2.2.2.2.2.2.2 = 128
3. 44 = 4.4.4.4 = 256
4. 73 = 7.7.7 = 343
6. 35 = 243
7. 26 = 64
8. 34 = 81
9. 83 = 512
11. 132 = 169
12. 112 = 121
13. 142 = 196
14. 152 = 225
16. 172 = 289
17. 182 = 324
18. 192 = 361
19. 202 = 400
21. 104 = 10000
22. 105 = 100000
23. 106 = 1000000
24. 107 = 10000000
- 22.32.5:22.3-32=3.5-32=15-9=6
- 2.52-22.32:32=2.(52-2)=2.(25-2)=46
3. 33.19-33.12=33.(19-12)=33.7=189
4. 3.52-16:22=3.52-24:22=3.25-4=75-4=71
a,\(5^3.2-100:4+2^3.5\)
= 125 . 2 - 25 + 8 . 5
= 250 - 25 + 40
= 265
b, \(6^2:9+50.2-3^3.3\)
= 36 : 9 + 100 - 27 . 3
= 4 + 100 - 81
= 23
1: \(=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{16}\cdot4=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{4}\)
\(=\dfrac{48}{56}+\dfrac{7}{56}-\dfrac{42}{56}=\dfrac{13}{56}\)
2: \(=-\dfrac{1}{6}+\dfrac{2}{3}\cdot\dfrac{-3}{4}+\dfrac{4}{5}\)
\(=\dfrac{19}{30}-\dfrac{1}{2}=\dfrac{19}{30}-\dfrac{15}{30}=\dfrac{4}{30}=\dfrac{2}{15}\)
3: \(=\dfrac{11}{4}\cdot\dfrac{-2}{5}+\dfrac{8}{5}\cdot\dfrac{7}{4}+\dfrac{-36}{5}\cdot\dfrac{11}{9}\)
\(=\dfrac{-22+56}{20}+\dfrac{-44}{5}\)
\(=\dfrac{-71}{10}\)
1) \(\frac{5}{8}.\frac{7}{3}-\frac{5}{2}.\frac{1}{8}=\frac{5}{8}.\frac{7}{3}-\frac{5}{8}.\frac{1}{2}=\frac{5}{8}\left(\frac{7}{3}-\frac{1}{2}\right)=\frac{5}{8}.\frac{11}{6}=\frac{55}{48}\)
2) \(\frac{21}{10}.\frac{3}{4}-\frac{21}{10}.\frac{3}{4}=\frac{21}{10}\left(\frac{3}{4}-\frac{3}{4}\right)=\frac{21}{10}.0=0\)
3) \(\frac{-4}{11}:\frac{-6}{11}=\frac{-4}{11}.\frac{-11}{6}=\frac{-4.\left(-11\right)}{11.6}=\frac{-4.\left(-1\right)}{1.6}=\frac{4}{6}=\frac{2}{3}\)
4)\(\frac{2}{7}.\frac{14}{3}-1=\frac{2.14}{7.3}-1=\frac{2.2}{1.3}-1=\frac{4}{3}-1=\frac{1}{3}\)
5)\(\frac{4}{7}:\left(\frac{1}{5}.\frac{4}{7}\right)=\frac{4}{7}:\frac{4}{35}=\frac{4}{7}.\frac{35}{4}=\frac{4.35}{7.4}=\frac{1.5}{1.1}=5\)
6) \(\frac{12}{7}.\frac{7}{4}+\frac{35}{11}:\frac{245}{121}=\frac{12.7}{7.4}+\frac{35}{11}.\frac{121}{245}=\frac{3.1}{1.1}+\frac{35}{11}.\frac{121}{245}=3+\frac{35}{11}.\frac{121}{245}=3+\frac{35.121}{11.245}=\frac{1.11}{1.7}=\frac{11}{7}\)
1: \(\dfrac{15}{7}\cdot\dfrac{-3}{21}=\dfrac{15}{21}\cdot\dfrac{-3}{7}=\dfrac{-3}{7}\cdot\dfrac{5}{7}=-\dfrac{15}{49}\)
2: \(\dfrac{34}{-11}\cdot\left(\dfrac{1}{3}-\dfrac{5}{6}\right)^2+\dfrac{10}{11}\cdot\left(0,125\right)\)
\(=\dfrac{-34}{11}\left(\dfrac{2}{6}-\dfrac{5}{6}\right)^2+\dfrac{10}{11}\cdot\dfrac{1}{8}\)
\(=\dfrac{-34}{11}\cdot\dfrac{1}{4}+\dfrac{10}{88}\)
\(=\dfrac{-34}{44}+\dfrac{10}{88}=\dfrac{-34}{44}+\dfrac{5}{44}=\dfrac{-29}{44}\)
3: \(\left(\dfrac{3}{5}-\dfrac{1}{15}\right)\cdot\dfrac{-8}{7}-\dfrac{1}{3}\left(\dfrac{1}{2}-\dfrac{1}{4}\right)^2\)
\(=\left(\dfrac{9}{15}-\dfrac{1}{15}\right)\cdot\dfrac{-8}{7}-\dfrac{1}{3}\left(\dfrac{1}{4}\right)^2\)
\(=\dfrac{8}{15}\cdot\dfrac{-8}{7}-\dfrac{1}{3}\cdot\dfrac{1}{16}\)
\(=-\dfrac{64}{105}-\dfrac{1}{48}=-\dfrac{353}{560}\)