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a/ \(63^7< 64^7=\left(4^3\right)^7=4^{21}\)
\(16^{12}=\left(4^2\right)^{12}=4^{24}\)
Suy ra \(63^7< 4^{21}< 4^{24}=16^{12}\)
Vậy \(63^7< 16^{12}\)
a) \(63^7\)và \(16^{12}\)
Có \(63^7< 64^7=\left(2^6\right)^7=2^{42}\)
\(16^{12}=\left(2^4\right)^{12}=2^{48}\)
Mà \(2^{42}< 2^{48}\Rightarrow63^7< 64^7< 16^{12}\)=) \(63^7< 16^{12}\)
b) \(17^{14}\)và \(31^{11}\)
Có \(17^{14}>16^{14}=\left(2^4\right)^{14}=2^{56}\)
\(31^{11}< 32^{11}=\left(2^5\right)^{11}=2^{55}\)
Vì \(2^{56}>2^{55}\Rightarrow17^{14}>16^{14}>32^{11}>31^{11}\)
=) \(17^{14}>31^{11}\)
c) \(2^{67}\)và \(5^{21}\)
Có \(5^{21}< 8^{21}=\left(2^3\right)^{21}=2^{63}\)
Vì \(2^{67}>2^{63}\Rightarrow2^{67}>8^{21}>5^{21}\)
=) \(2^{67}>5^{21}\)
a,\(2^{31}=2^{30}.2=\left(2^3\right)^{10}.2=8^{10}.2< 9^{10}.3=\left(3^2\right)^{10}.3=3^{20}.3=3^{21}\)
b,\(2^{99}=\left(2^3\right)^{33}=8^{33}>3^{21}\)
c,\(31^{14}< 32^{14}=\left(2^5\right)^{14}=2^{70}< 2^{72}=\left(2^4\right)^{18}=16^{18}< 17^{18}\)
d,\(63^{10}< 64^{10}=\left(2^6\right)^{10}=2^{60}< 2^{65}=\left(2^5\right)^{13}=32^{13}< 33^{13}\)
Nguyễn Đăng Duy ơi bài trên là tính nhanh hay tính vậy bạn .
a, \(4^{100}=\left(2^2\right)^{100}=2^{200}< 2^{202}\)
\(\Rightarrow\text{ }4^{100}< 2^{202}\)
b, \(3^0=1< 5^8\)
\(3^0< 5^8\)
c, \(\left(0,6\right)^0=1\)
\(\left(-0,9\right)^6=\left(0,9\right)^6\)
\(\Rightarrow\text{ }\left(0,6\right)^0< \left(-0,9\right)^6\)
d,
e, \(8^{12}=\left(2^3\right)^{12}=2^{36}=2^{16}\cdot2^{20}=2^{16}\cdot\left(2^4\right)^5=2^{16}\cdot16^5\)
\(12^8=\left(2^2\cdot3\right)^8=2^{16}\cdot3^8=2^{16}\cdot\left(3^2\right)^4=2^{16}\cdot9^4\)
Vì \(2^{16}\cdot16^5>2^{16}\cdot9^4\text{ }\Rightarrow\text{ }8^{12}>12^8\)
a) 275=(33)5=315
2433=(35)3=315
vì 315=315 nên 275=2433
b) 2300=(23)100=8100
3200=(32)100=9100
vì 8100>9100 nên 2300>3200
\(63^7< 64^7=\left(2^6\right)^7=2^{42};16^{12}=\left(2^4\right)^{12}=2^{48}\Rightarrow63^7< 16^{12}\)
\(17^{14}>16^{14}=\left(2^4\right)^{14}=2^{56};31^{11}< 32^{11}=\left(2^5\right)^{11}=2^{55}\Rightarrow17^{14}>31^{11}\)
\(2^{67}=2^{63}.16=128^9.16;5^{21}=125^7\Rightarrow2^{67}>5^{21}\)
\(2^{100}=1024^{10};10^{30}=1000^{10}\Rightarrow\frac{2^{10}}{10^3}=\frac{128}{125}< \frac{20}{19}< \frac{19}{18}< .....< \frac{11}{10}\Rightarrow\frac{2^{100}}{10^3}=\left(\frac{2^{10}}{10^3}\right)^{10}< \frac{20}{19}.\frac{19}{18}.....\frac{11}{10}=2\Rightarrow2^{100}< 2.10^{30}< 10.10^{30}=10^{31}\)