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a, 273 : 35 = ( 33)3 : 35 = 39 : 35 = 34
b, 72 . 343 . 4930 = 72. 73.(72)3 = 711
c, 625 : 53 = 54 : 53 = 5
d, 1 000 000 : 103 = 106 . 103 = 103
e, 115 : 121= 115 : 112 = 113
f, 87 : 64 :8 = 87 : 82 : 81 = 84
i, 1024 . 16 : 26 = 210 . 23 : 26 = 27
1.
a) \(3^4\times3^5\times3^6=3^{4+5+6}=3^{15}\)
b) \(5^2\times5^4\times5^5\times25=5^2\times5^4\times5^5\times5^2=5^{2+4+5+2}=5^{13}\)
c) \(10^8\div10^3=10^{8-3}=10^5\)
d) \(a^7\div a^2=a^{7-2}=a^5\)
2.
\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)
\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)
\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)
a)
\({5^7}{.5^5} = 5^{7+5}={5^{12}}\)
\({9^5} :{8^0} = {9^5}:1 = {9^5}\)
\(2^{10}:64.16 = 2^{10}:2^6.2^4 = 2^{10-6+4} = 2^8\)
b)
\(\begin{array}{l}54297 = 5.10000 + 4.1000 + 2.100 + 9.10 + 7\\ = {5.10^4} + {4.10^3} + {2.10^2} + 9.10 + 7\end{array}\)
\(\begin{array}{l}2023 = 2.1000 +0.100+2.10 + 3\\ = {2.10^3}+ 2.10 +3\end{array}\)
a, 48.84
= (22)8.(23)4
= 216.212
= 228
b, 415.515
= (4.5)15
= 2015
c, 210.15 + 210.85
= 210.(15 + 85)
= 210.100
=210.(2.5)2
= 212.52
d, 33.92
= 33 . (32)2
= 33.34
= 37
e, 512.7 - 511.10
= 511.(5.7 - 10)
= 511.25
=511.52
=513
f, \(x^1\).\(x^2\).\(x^3\)....\(x^{100}\)
= \(x^{1+2+3+...+100}\)
= \(x^{\left(1+100\right).100:2}\)
= \(x^{5050}\)
Bg
a) 43 ÷ 25 = (22)3 ÷ 25
= 22.3 ÷ 25
= 26 ÷ 25
= 26 - 5
= 21
= 2
b) 97 ÷ 32 = 97 ÷ 9
= 97 ÷ 91
= 97 - 1
= 96
c) 2.22.23.24. … .2100
= 21 + 2 + 3 + 4 +…+ 100
Đặt A = 1 + 2 + 3 + 4 +…+ 100 (A có 100 số hạng)
=> A = \(\frac{100.\left(100+1\right)}{2}\)
=> A = \(\frac{100.101}{2}\)
=> A = \(\frac{10100}{2}\)
=> A = 5050
Quay lại với đề bài:
= 25050
a ) \(4^3\div2^5=2^6\div2^5=2^1\)
b ) \(9^7\div3^2=9^7\div9=9^6\)
c ) \(2.2^2.2^3.2^4....2^{100}=2^{1+2+3+....+100}\)
Ta có : \(1+2+3+....+100=\frac{\left(100+1\right).100}{2}=5050\)
\(\Rightarrow2^{1+2+3+....+100}=2^{5050}\)
1a) 7^4 b) 15^4 c) 1000^2 d)a^3.b^3
e)m^4+p^2 f)a^7-a^2.b^2
2)a)2^6 b) 5^8 c) 3^10 d)3^14
e) a^6 f)b^5