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Ta có
37.275.813 \(=\)\(3^7.3^{15}.3^{12}=3^{34}\)
365:185 \(=18^5\times2^5:18^5=2^5\)
24.55+52.53 \(=24.5^5+5^5=\left(24+1\right)5^5=25.5^5=5^7\)
1254:58\(=5^{12}:5^8=5^4\)
a) \(4.5^2-81:3^2=4.25-81:9=100-9=91\)
b) \(3^3.23-3^3.19=3^3.\left(23-19\right)=27.4=108\)
c) \(2^4.5-[131-\left(13-4\right)^2]=16.5-\left(131-9^2\right)=80-\left(131-81\right)=80-50=30\)
d) \(100:\left\{250:\left[450-\left(4.5^3-2^2.25\right)\right]\right\}\)
\(=100:\left\{250:\left[450-4.\left(125-25\right)\right]\right\}\)
\(=100:\left[250:\left(450-4.100\right)\right]\)
\(=100:\left[250:\left(450-400\right)\right]=100:\left(250:50\right)=100:5=20\)
\(5^6\text{ : }5^4+2^3\cdot2^2-1^{2017}\)
\(=5^2+2^5-1\)
\(=25-32-1\)
\(=-7-1\)
\(=-8\)
72-36:32
=49-36:9
=49-4
=45
70-[60-(12-8)2]
=70-(60-42)
=70-(60-16)
=70-44
=26
24.5-[131-(13-4)2]
=16.5-(131-92)
=16.5-(131-81)
=16.5-50
=80-50
=30
\(b,\left(1^2+2^3+3^4+4^5\right).\left(1^3+2^3+3^3+4^3\right).\left(3^8-81^2\right)\)
\(=\left(1^2+2^3+3^4+4^5\right).\left(1^3+2^3+3^3+4^3\right).\left[3^8-\left(3^4\right)^2\right]\)
\(=\left(1^2+2^3+3^4+4^5\right).\left(1^3+2^3+3^3+4^3\right).\left(3^8-3^8\right)\)
\(=\left(1^2+2^3+3^4+4^5\right)\left(1^3+2^3+3^3+4^3\right).0=0\)
a, = 71995 . ( 72 - 1) : 71995 = 49 - 1 = 48
b, = ........... x ( 38 - 38) = 0
Bài 1:
1. 36.7 + 34.37 + 19.100
= 34.(32.7 + 37) + 19.100
= 81.100 + 19.100
= 100.(81 + 19)
= 100.100
= 10000
2) 2.14.98+7.4.32-28.30
= 28.98 + 28.32 - 28.30
= 28. (98 + 32 - 30)
= 28.100
= 2800
3) (56.35+56.18):53
= [56.(35 + 18)] : 53
= 56.53:53
= 56
4) (158.129-158.39):28
= [158. (129 - 39)] : 28
= 158.90:28
= 5,675
4 . 52+ 81 : 32 - ( 13 - 4 )2
= 4 . 25 + 81 : 9 - 9\(^2\)
= 100 + 9 - 81
= 28