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2300 và 3200
Ta rút thử thành 23 và 32
23 = 2.2.2 = 8
32 = 3.3 = 9
Vì 23 < 32 nên 2300 < 3200
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9^27=3^81 > 81^13 =3^52
5^14 =25^7 < 27^7
10^30>9^30=3^90 > 2^100 (chú ý 3^3>2^4)
2^300=8^100 < 3^200=9^100
8^5=2^15=2^6.2^9 < 2^6.3^6 (chú ý 2^3<3^2)
3^450=(3^3)^150=27^150 > 5^300=(5^2)^150=25^150
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a) 13^1 <13^15
b)7^3 < 8^3
c) 7 - 6 = 13-12
d) 2^300 <3^200
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Ta có :
2300 = ( 23 )100 = 8100
3200 = ( 32 )100 = 9100
Vì 8100 < 9100 nên 2300 < 3200
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\(a,\)\(\text{Ta có: }\) \(3^{200}=\left(3^2\right)^{100}=9^{100}\left(1\right)\)
\(2^{300}=\left(2^3\right)^{100}=8^{100}\left(2\right)\)
\(\text{Từ (1) và (2) }\)\(\Rightarrow3^{200}>2^{300}\)
a, 3^200= (3^2)^100= 9^100
2^300= (2^3)^100= 8^100
Vì 9^100>8^100 nên 3^200>2^300
b, 125^5= (5^3)^5= 5^15
25^7= (5^2)^7= 5^14
Vì 5^15>5^14 nên 125^5>25^7
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7^2.7^3-3^3:3^0
=7^5-27
=16807-27
=16789
ta có 2^300=(2^30)^100=8^100
3^200=(3^2)^100=9^100
Vì 8<9 suy ra 2^300<3^200
(k mk nha)