Bài 1:
a) Ta có: \(1000\cdot25\cdot4\)
\(=10^3\cdot10^2\)
\(=10^5\)
b) Ta có: \(32\cdot24\cdot243\)
\(=2^5\cdot2^3\cdot3\cdot3^5\)
\(=2^8\cdot3^6\)
\(=6^6\cdot2^2\)
\(=\left(6^3\right)^2\cdot2^2\)
\(=\left(6^3\cdot2\right)^2=432^2\)
c) Ta có: \(8\cdot9\cdot10\cdot125\)
\(=2^3\cdot3^2\cdot2\cdot5\cdot5^3\)
\(=2^4\cdot3^2\cdot5^4\)
\(=\left(10^2\right)^2\cdot3^2\)
\(=\left(10^2\cdot3\right)^2\)
\(=300^2\)
d) Ta có: \(6^{15}\cdot6^{21}\cdot36\)
\(=6^{15}\cdot6^{21}\cdot6^2\)
\(=6^{38}\)
e) Ta có: \(\frac{5^{2019}}{5^{2000}}\cdot625\)
\(=5^{19}\cdot5^4=5^{23}\)
Bài 2:
a) Ta có: 57<75
nên \(29^{57}< 29^{75}\)
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