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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=9.10^2+8.10^1+7.10^0
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...
987= 10^2. 9+ 10.8+ 10^0. 7
2564= 10^3. 2+ 10^2 . 5+ 10.6 + 10^0. 4
abcde= 10^4.a+ 10^3.b+10^2.c+10.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
987 = 9 . 100 + 8 . 10 + 7
= 9 . 102 + 8 . 101 + 7 . 100
2564 = 2 . 1000 + 5 . 100 + 6 . 10 + 4
= 2 . 103 + 5 . 102 + 6 . 101 + 4 . 100
abcde = a . 10 000 + b . 1000 + c . 100 + d . 10 + e
= a . 104 + b . 103 + c . 102 + d . 101 + e . 100
987=9.100+8.10+7.1=9.102+8.101+7.100
2564=2.1000+5.100+6.10+4.1=2.103+5.102+6.101+4.100
abcde=a.10000+b.1000+c.100+d.10+e.1=a.104+b.103+c.102+d.101+e.100
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
