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a. Ta có:
\(72^{45}-72^{44}=72^{44}.\left(72-1\right)=72^{44}.71\)
\(72^{44}-72^{43}=72^{43}.\left(72-1\right)=72^{43}.71\)
Vì \(72^{44}.71>72^{43}.71\)
\(\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}\)
\(A = 1 + 2 + 2^2 + 2^3+ ... + 2^{63}\)
\(2A=2+2^2+2^3+...+2^{63}+2^{64}\)
\(2A-A=2+2^2+2^3+...+2^{63}+2^{64}-\left(1+2+2^2+2^3+...+2^{63}\right)\)
\(\Rightarrow A=2^{64}-1\)
125(28+72)-25(3^2.4+64)
=125.100-25(9.4+64)
=125.100-25.(36+64)
=125.100-25.100
=12500-2500
=10000
a/ \(A=\dfrac{4^{10}.64^2}{16^3}=\dfrac{\left(2^2\right)^{10}.\left(2^6\right)^2}{\left(2^4\right)^3}=\dfrac{2^{20}.2^{12}}{2^{12}}=2^{20}\)
b/ \(B=\dfrac{27^8}{9^{11}.3^0}=\dfrac{\left(3^3\right)^8}{\left(3^2\right)^{11}.3^0}=\dfrac{3^{24}}{3^{22}}=3^2=9\)
c/ \(C=\dfrac{3^8.4+3^8.9}{3^8.13}=\dfrac{3^8\left(4+9\right)}{3^8.13}=\dfrac{3^8.13}{3^8.13}=1\)
\(5^8:25^2=5^8:5^4\)
=54=625
\(4^9:64^2=4^9:\left(2^2\right)^6\)
=49:46
=43=64
58 : 252 = 58 : (52)2
= 58 : 54
= 54
49 : 642 = 49 : (43)2
= 49 : 46
= 43