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Câu 1:
a) 2225 và 3150
Ta có:2225=(29)25=51225
3150=(36)25=72925
Vì 51225<72925
Suy ra: 2225<3150
Câu 2:
a)\(25^3:5^2=\left(5^2\right)^3:5^2=5^6:5^2=5^4\)
b)\(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{21}:\left[\left(\frac{3}{7}\right)^2\right]^6=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{12}=\left(\frac{3}{7}\right)^9\)
c)\(3-\left(-\frac{6}{7}\right)^0+\left(\frac{1}{2}\right)^2:2=3+\frac{1}{4}:2=3+\frac{1}{8}=\frac{25}{8}\)
Câu 3:
a)\(9.3^3.\frac{1}{81}.3^2=3^2.3^3.3^2.\left(\frac{1}{3^4}\right)=3^7:3^4=3^3\)
b)\(4.2^5:\left(2^3.\frac{1}{16}\right)=2^2.2^5:\left(2^3.\frac{1}{2^4}\right)=2^7:\frac{1}{2}=2^8\)
c)\(3^2.2^5.\left(\frac{2}{3}\right)^2=288.\frac{4}{9}=2^7\)
d)\(\left(\frac{1}{3}\right)^3.\frac{1}{3}.9^2=\left(\frac{1}{3}\right)^4.\left(3^2\right)^2=3^4.\left(\frac{1}{3}\right)^4=3^4:3^4=1\)
\(a,20^8.4^8=\left(20.4\right)^8=80^8\)
\(b,10^6:2^6=\left(10:2\right)^6=5^6\)
\(c,5^4.2^8=5^4.\left(2^2\right)^4=5^4.4^4=\left(5.4\right)^4=20^4\)
\(d,7^8.9^4=7^8.\left(3^2\right)^4=7^8.3^8=\left(7.3\right)^8=21^8\)
\(e,27^4:25^6=\left(3^3\right)^4:\left(5^2\right)^6=3^{12}:5^{12}=\left(3:5\right)^{12}=\left(\frac{3}{5}\right)^{12}\)
a) 814=(23)14=23*14=242
1610=(8*2)10=810*210=(23)10*210=230*210=240
Vì 242 > 240 nên 814 > 1610
b) 233=(23)11=811
322=(32)11=911
Vì 811 < 911 nên 233 < 322
45^10.5^20/75^15=243
0.8^5/0.4^6=80
2^15=9^4/6^6x8^3=9
1/3=3^-1
1/9=3^-2
99.99=9801<9999=>99^20<9999^10