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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.
\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)
\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)
\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)
8=2^3 ; 20=20^1 ; 60=60^1 ; 90=90^1
16=2^4 ; 27=3^3 ; 81=3^4 ; 100=10^2
a, 34.275.(32)3 = 34.(33)5.36 = 34.315.36 = 325
b, (23)4.46.32 = 212.212.25 = 229
c, 32019.62019: 22019 = 32019.32019.22019:22019 = (3.3)2019= 92019
d, 1258.(52)4 = (53)8.58 = 532
a) \(3^3.3^4=3^{3+4}=3^7\)
b) \(5^2.5^7=5^{2+7}=5^9\)
c) \(7^5.7=7^{5+1}=7^6\)
\(3^3.3^4=3^{3+4}=3^7\)
\(5^2.5^7=5^{2+7}=5^9\)
\(7^5.7=7^{5+1}=7^6\)
