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a ) 6 4 : 2 3 = 2 6 - 2 3 = 2 3 b ) 243 : 3 4 = 3 5 : 3 4 = 3 1 c ) 635 : 5 3 = 5 4 : 5 3 = 5 1 d ) 7 5 : 343 = 7 5 : 7 3 = 7 2
a, 8 2 . 32 4 = 2 3 2 . 2 5 4 = 2 3 . 2 . 2 5 . 4 = 2 6 . 2 20 = 2 6 + 20 = 2 26
b, 27 4 . 9 3 . 243 = 3 3 4 . 3 2 3 . 3 5 = 3 3 . 4 . 3 2 . 3 . 3 5 = 3 12 . 3 6 . 3 5 = 3 12 + 6 + 5 = 3 23
c, 13 2 - 12 2 = 169 - 144 = 25 = 5 2
d, 6 2 + 8 2 = 36 + 64 = 100 = 10 2
e, 5 3 + 5 4 + 125 2 . 5 3 = 5 3 + 5 4 + 5 3 . 2 . 5 3 = 5 3 + 5 4 + 5 6 . 5 3 = 5 3 . 1 + 5 + 5 3 . 5 3 = 5 6 . 131
f, 1 3 + 2 3 + 3 3 + 4 3 + 5 3 = 1 + 8 + 27 + 64 + 125 = 225 = 15 2
a, 64 : 2 3 = 2 6 : 2 3 = 2 3
b, 243 : 3 4 = 3 5 : 3 4 = 3 1
c, 625 : 5 3 = 5 4 : 5 3 = 5 1
d, 7 5 : 343 = 7 5 : 7 3 = 7 2
e, 100000 : 10 3 = 10 5 : 10 3 = 10 2
f, 11 5 : 121 = 11 5 : 11 2 = 11 3
g, 243 : 3 3 : 3 = 3 5 : 3 3 : 3 = 3 1
h, 4 8 : 64 : 16 = 4 8 : 4 3 : 4 2 = 4 3
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.
\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)
\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)
\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)
\(a,5^{200}:5^{13}=5^{200-13}=5^{187}\)
\(b,7^{2001}:7=7^{2001-1}=7^{2000}\)
\(c,16^{137}:4^2=16^{137}:16=16^{137-1}=16^{136}\)
\(d,\left(2^{48}\cdot2^5\right):\left(2^3\cdot2^{17}\right)=2^{48+5}:2^{3+17}=2^{53}:2^{10}=2^{53-10}=2^{43}\)
5200 : 513
= 5187
72001 : 7
= 72000