1){(-2/3)^2 + (1/2)^3} : 41/27
2)4.(-1/2)^3 -2.(-1/2)^2 + 3.(-1/2)
3)(1+2/3+14/9 ) : (5/6 - 4/5 )^2
4)2/7 - 3/2 . {19/25 + (-1,2)^2}
5)11/6 + (4/5 - 0,7 )^2 : (-3/5)
6)81^16 . 9^5/27^7 . 3^11
7)25^7 . 8^15 / 125^5 .24^7
8)2^3 . (0,5)^3 .3^7/2.(0,5)^4 .3^8
9)(-3)^10 . (-5)^21/(-5)20.3^12
10)10^3 +5+10^2+5^3/6^3+3.6^2+3^3

Question

Accepted Answer

1) Ta có:
$$ 
\left( -\frac{2}{3} \right)^2 + \left( \frac{1}{2} \right)^3 = \frac{4}{9} + \frac{1}{8} = \frac{32}{72} + \frac{9}{72} = \frac{41}{72}
$$
Do đó:
$$ 
\left( \frac{41}{72} \right) : \frac{41}{27} = \frac{41}{72} \times \frac{27}{41} = \frac{27}{72} = \frac{3}{8}
$$

2) Ta có:
$$ 
4 \times \left( -\frac{1}{2} \right)^3 - 2 \times \left( -\frac{1}{2} \right)^2 + 3 \times \left( -\frac{1}{2} \right) = 4 \times \left( -\frac{1}{8} \right) - 2 \times \frac{1}{4} + 3 \times \left( -\frac{1}{2} \right) = -\frac{4}{8} - \frac{2}{4} - \frac{3}{2} = -\frac{1}{2} - \frac{1}{2} - \frac{3}{2} = -\frac{5}{2}
$$

3) Ta có:
$$ 
1 + \frac{2}{3} + \frac{14}{9} = \frac{9}{9} + \frac{6}{9} + \frac{14}{9} = \frac{29}{9}
$$
$$ 
\left( \frac{5}{6} - \frac{4}{5} \right)^2 = \left( \frac{25}{30} - \frac{24}{30} \right)^2 = \left( \frac{1}{30} \right)^2 = \frac{1}{900}
$$
Do đó:
$$ 
\frac{29}{9} : \frac{1}{900} = \frac{29}{9} \times 900 = 2900
$$

4) Ta có:
$$ 
\frac{19}{25} + (-1,2)^2 = \frac{19}{25} + 1,44 = \frac{19}{25} + \frac{36}{25} = \frac{55}{25} = \frac{11}{5}
$$
Do đó:
$$ 
\frac{2}{7} - \frac{3}{2} \times \frac{11}{5} = \frac{2}{7} - \frac{33}{10} = \frac{20}{70} - \frac{231}{70} = -\frac{211}{70}
$$

5) Ta có:
$$ 
\frac{4}{5} - 0,7 = \frac{4}{5} - \frac{7}{10} = \frac{8}{10} - \frac{7}{10} = \frac{1}{10}
$$
Do đó:
$$ 
\frac{11}{6} + \left( \frac{1}{10} \right)^2 : \left( -\frac{3}{5} \right) = \frac{11}{6} + \frac{1}{100} : \left( -\frac{3}{5} \right) = \frac{11}{6} + \frac{1}{100} \times \left( -\frac{5}{3} \right) = \frac{11}{6} - \frac{1}{60} = \frac{110}{60} - \frac{1}{60} = \frac{109}{60}
$$

6) Ta có:
$$ 
81^{16} \times 9^5 : 27^7 \times 3^{11} = (3^4)^{16} \times (3^2)^5 : (3^3)^7 \times 3^{11} = 3^{64} \times 3^{10} : 3^{21} \times 3^{11} = 3^{64+10-21-11} = 3^{42}
$$

7) Ta có:
$$ 
25^7 \times 8^{15} : 125^5 \times 24^7 = (5^2)^7 \times (2^3)^{15} : (5^3)^5 \times (2^3 \times 3)^7 = 5^{14} \times 2^{45} : 5^{15} \times 2^{21} \times 3^7 = 5^{14-15} \times 2^{45-21} \times 3^{-7} = 5^{-1} \times 2^{24} \times 3^{-7} = \frac{2^{24}}{5 \times 3^7}
$$

8) Ta có:
$$ 
2^3 \times (0,5)^3 \times 3^7 : 2 \times (0,5)^4 \times 3^8 = 2^3 \times \left( \frac{1}{2} \right)^3 \times 3^7 : 2 \times \left( \frac{1}{2} \right)^4 \times 3^8 = 2^3 \times \frac{1}{2^3} \times 3^7 : 2 \times \frac{1}{2^4} \times 3^8 = 1 \times 3^7 : \frac{1}{2^3} \times 3^8 = 3^7 \times 2^3 : 3^8 = 2^3 : 3 = \frac{8}{3}
$$

9) Ta có:
$$ 
(-3)^{10} \times (-5)^{21} : (-5)^{20} \times 3^{12} = 3^{10} \times (-5) \times 3^{-12} = 3^{10-12} \times (-5) = 3^{-2} \times (-5) = \frac{-5}{9}
$$

10) Ta có:
$$ 
10^3 + 5 + 10^2 + 5^3 = 1000 + 5 + 100 + 125 = 1130
$$
$$ 
6^3 + 3 \times 6^2 + 3^3 = 216 + 108 + 27 = 351
$$
Do đó:
$$ 
\frac{1130}{351} = \frac{1130}{351}
$$

1){(-2/3)^2 + (1/2)^3} : 41/27 2)4.(-1/2)^3 -2.(-1/2)^2 + 3.(-1/2) 3)(1+2/3+14/9 ) : (5/6 - 4/5 )^2 4)2/7 - 3/2 . {19/25 + (-1,2)^2} 5)11/6 + (4/5 - 0,7 )^2 : (-3/5) 6)81^16 . 9^5/27^7 . 3^11 7)25^7 ....