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a) Ta có:
\(2^{3000} = (2^3)^{1000} = 8^{1000} \)
\(3^{2000} = (3^2)^{1000} = 9^{1000}\)
Vì \(8<9\) nên \(8^{1000}<9^{1000}\)
Vậy \(2^{3000}<3^{2000}\)
Ta có:
\(2^{91}=\left(2^{13}\right)^7=8192^7\)
\(5^{35}=\left(5^5\right)^7=3125^7\)
Vì \(8192^7>3125^7\left(8125>3125\right)\) nên \(2^{91}>5^{35}\)
Vậy \(2^{91}>5^{35}\)