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a) $125^3:25^4=(5^3)^3:(5^2)^4=5^9:5^8=5^1$
$16^4:4^2=(4^2)^4:4^2=4^8:4^2=4^6$
$27^8:9^4=(3^3)^8:(3^2)^4=3^{24}:3^8=3^{16}$
$125^5:25^3=(5^3)^5:(5^2)^3=5^{15}:5^6=5^9$
$4^{14}:5^{28}=(2^2)^{14}:5^{28}=2^{28}:5^{28}=(\dfrac{2}{5})^{28}$
b) $12^n:2^{2n}=12^n:(2^2)^n=12^n:4^n=3^n$
$64^4.16^5.4^{20}=(4^3)^4.(4^2)^5.4^{20}=4^{12}.4^{10}.4^{20}=4^{42}$
\(12^n\times2^{2n}\)
= \(12^n\times4^n\)
= \(\left(12\times4\right)^n\)
\(48^n\)
4 mũ 2 = 2 mũ 3 nên 2 mũ 15. 4 mũ 2 = 2 mũ 15. 2 mũ 3 = 2 mũ 18
3 mũ 2 =9 mũ 1 nên9 mũ 12.3 mũ 2 =9 mũ 12. 9 mũ 1 = 9 mũ 11
225.42= 225 . (22)2 = 225. 24 = 229
912: 32 = (32)12: 32= 324: 32 = 322
\(8^{2n}:4^{3n}\)
\(=\left(2^3\right)^{2n}:\left(2^2\right)^{3n}\)
\(=2^{6n}:2^{6n}\)
\(=2^{6n-6n}\)
Ta có :
\(14^4.4^2.21^5.28^3.18^3\)
\(=\left(7.2\right)^{14}.\left(2^2\right)^2.\left(7.3\right)^5.\left(7.2^2\right)^3.\left(3^2.2\right)^3\)
\(=7^{14}.2^{14}.2^4.7^5.3^5.7^3.2^6.3^6.2^3\)
\(=\left(7^{14}.7^5.7^3\right)\left(2^{14}.2^4.2^6.2^3\right)\left(3^5.3^6\right)\)
\(=7^{22}.2^{27}.3^{11}\)
\(8^5.2^3:2^4\)
\(=\left(2^3\right)^5.2^3:2^4\)
\(=2^{15}.2^3:2^4\)
\(=2^{18}:2^4=2^{14}=16384\)
a)414.528
=414.(52)14
=414.2514
=(4.25)14=10014
b)12n:22n
=12n:(22)n
=12n:4n
=(12:4)n=3n
thanks