Ta có: 

\(5^{217}>5^{216}\)

Mà: \(5^{216}=5^{3\cdot72}=\left(5^3\right)^{72}=125^{72}\)

Lại có: \(125>119\Rightarrow125^{72}>119^{72}\)

\(\Rightarrow5^{216}>119^{72}\)

\(\Rightarrow5^{217}>119^{72}\)

a. \(5^{127}=5.5^{126}=5.125^{72}>119^{72}\)

\(\Rightarrow5^{217}>119^{72}\)

b. \(2^{1000}=\left(2^5\right)^{200}=32^{200}\)

\(5^{400}=\left(5^2\right)^{200}=25^{200}\)

\(\Rightarrow2^{1000}>5^{400}\)

c. \(9^{12}=\left(3^2\right)^{12}=3^{24}\)

\(27^7=\left(3^3\right)^7=3^{21}\)

\(\Rightarrow9^{12}>27^7\)

d. \(125^{80}=\left(5^3\right)^{80}=5^{240}\)

\(25^{118}=\left(5^2\right)^{118}=5^{236}\)

\(\Rightarrow125^{80}>25^{118}\)

e. \(5^{40}=\left(5^4\right)^{10}=625^{10}\)

\(\Rightarrow5^{40}>620^{10}\)

f. \(27^{11}=\left(3^3\right)^{11}=3^{33}\)

\(81^8=\left(3^4\right)^8=3^{32}\)

\(\Rightarrow27^{11}>81^8\)

a) \(2^{300}=\left(2^3\right)^{100}=8^{100}\)

\(3^{200}=\left(3^2\right)^{100}=9^{100}>8^{100}\)

\(\Rightarrow2^{300}< 3^{200}\)

b) \(99^{20}=\left(99^2\right)^{10}=9801^{10}< 9999^{10}\Rightarrow99^{20}< 9999^{10}\)

c) \(3^{500}=\left(3^5\right)^{100}=243^{100}\)

\(7^{300}=\left(7^3\right)^{100}=343^{100}>243^{100}\)

\(\Rightarrow3^{500}< 7^{300}\)

Giải chi tiết giúp mình ạ~

\(\left(d\right):202^{303}=\left(202^3\right)^{101}=8242408^{101}>303^{202}=\left(303^2\right)^{101}=91809^{101}\)

\(\left(e\right):107^{50}=\left(107^2\right)^{25}=11449^{25}< 73^{75}=\left(73^3\right)^{25}=389017^{25}\)

\(5^{300}>3^{547}\)

5 ^ 300 < 3 ^ 547

a: \(\dfrac{-2}{37}=\dfrac{-82}{37\cdot41}\)

\(\dfrac{-3}{41}=\dfrac{-3\cdot37}{41\cdot37}=\dfrac{-111}{41\cdot37}\)

mà -82>-111

nên \(-\dfrac{2}{37}>-\dfrac{3}{41}\)

b: \(\dfrac{57}{47}=1+\dfrac{10}{47}\)

\(\dfrac{557}{547}=1+\dfrac{10}{547}\)

mà 10/47>10/547

nên \(\dfrac{57}{47}>\dfrac{557}{547}\)

hay \(-\dfrac{57}{47}< -\dfrac{557}{447}\)

c: \(\dfrac{139}{155}=1-\dfrac{16}{155}\)

\(\dfrac{141}{157}=1-\dfrac{16}{157}\)

mà 16/155>16/157

nên \(\dfrac{139}{155}< \dfrac{141}{157}\)

Vì \(37< 46\) nên \(\frac{278}{37}>\frac{287}{46}\)

Ta có: 

\(\frac{547}{216}-2=\frac{115}{216}\)

\(\frac{546}{215}-2=\frac{116}{215}\)

Vì \(\frac{115}{216}< \frac{116}{215}\) nên \(\frac{547}{216}< \frac{546}{215}\)

a) \(\frac{278}{37}=7+\frac{19}{37}\)   \(\frac{287}{46}=7-\frac{35}{46}\)

\(\frac{278}{37}>7>\frac{287}{46}\Rightarrow\frac{278}{37}>\frac{287}{46}\)

b) Ta có: \(\frac{547}{216}=1+\frac{331}{216}\)

                 \(\frac{546}{215}=1+\frac{331}{215}\)

mà \(\frac{331}{216}< \frac{331}{215}\)

=> \(\frac{547}{216}< \frac{546}{215}\)

So sánh phần hơn đó!

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