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123 = 10^2+10^1 . 2 + 10^0 . 3
2355 = 10^3 . 2 + 10^2 . 3 + 10^1 . 5 + 10^0.5
abcde = 10^4 . a + 10^3 . b + 10^2 . c + 10^1 . d + 10^0 . e
987 = 9 . 102 + 8 . 10 + 7;
2564 = 2 . 103 + 5 . 102 + 6 . 10 + 4;
abcde = a . 104 + b . 103 + c . 102 + d . 10 + e
987 = 9 . 102 + 8 . 10 + 7;
2564 = 2 . 103 + 5 . 102 + 6 . 10 + 4;
abcde = a . 104 + b . 103 + c . 102 + d . 10 + e
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.
\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)
\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)
\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)
987=9.100+8.10+7.1=9.102+8.10+7.100
2564=2.1000+5.100+6.10+4.1=2.103+5.102+6.10+4.100
abcde=a.10000+b.1000+c.100+d.10+e.1=a.104+b.103+c.102+d.10+e.100
987=900+80+7=9.100+8.10+7.1=9.102+8.101+7.100
2564=2000+500+60+4=2.1000+5.100+6.10+4.1=2.103+5.102+6.101+4.100
abcde=10000.a+1000.b+100.c+10.d+1.e=104.a+103.b+102.c+101.d+100.e
987=9.102+8.101+7.100
2564=2.10^3+5.10^2+6.10^1+4.10^0
abcde=a.10^4+b.10^3+c.10^2+d.10^1+e.10^0
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