Ta có
4825<6425=(26)25=2150
851=(23)51=2153
Mà 2153>2150>4825
=)2153>4825
=)851>4825
Ta có:\(48^{25}=\left[\left(\sqrt{48}\right)^2\right]^{25}=\left(\sqrt{48}\right)^{50}\)
\(8^{51}=\left(\sqrt{64}\right)^{51}\)
Vì \(\hept{\begin{cases}\sqrt{64}>\sqrt{48}\\51>50\end{cases}}\)nên \(\left(\sqrt{64}\right)^{51}>\left(\sqrt{48}\right)^{50}\)
hay \(48^{25}>8^{51}\)
\(48^{25}=\left(16.3\right)^{25}=\left(2^4.3\right)^{25}=2^{100}.3^{25}\)
\(8^{51}=\left(2^2.3\right)^{51}=2^{102}.3^{51}\)
Vì \(2^{100}.3^{25}< 2^{102}.3^{51}\Rightarrow4^{25}< 8^{51}\)
Phạm Thị Thùy Linh\(8^{51}\ne\left(2^2.3\right)^{51}\)vì \(2^2.3=12\)
