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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.
\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)
\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)
\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)
\(5.p.p.5.p^2.q.4.q=\left(5.5.4\right).\left(p.p.p^2\right).\left(q.q\right)=100p^4.q^2\)
\(a,3^7.27^5.81^3\\ =3^7.\left(3^3\right)^5.\left(3^4\right)^3\\ =3^7.3^{15}.3^{12}\\ =3^{34}\\ b,100^6.1000^5.10000^4\\ =100^6.100^{10}.100^{12}\\ =100^{28}\\ c,125^4:5^8\\ =5^{12}:5^8\\ =5^4.\)
\(8^5.2^3:2^4\)
\(=\left(2^3\right)^5.2^3:2^4\)
\(=2^{15}.2^3:2^4\)
\(=2^{18}:2^4=2^{14}=16384\)
l) 27^8=(33)8=324
=>278:322=324:322
=324-22=32
m) 8^4=(23)4=212
45=(22)5=210
=>84:45=212:210
=212-10=22
a) \(27^8:3^{22}\)
\(=\left(3^3\right)^8:3^{22}\)
\(=3^{24}:3^{22}=3^{24-22}\)
\(=3^2\)
b) \(8^4:4^5\)
\(=\left(2^3\right)^4:\left(2^2\right)^5\)
\(=2^{12}:2^{10}=2^{12-10}=2^2\)
\(2^5.8^4=2^5.\left(2^3\right)^4=2^5.2^{12}=2^{17}\)
25.84=25.212=217