3 mũ 34 lớn hơn 5 mũ 20

Ta có: a) 3^34 = (3^8 )^4 = 6561^4

5^20 = ( 5^4 )^4= 3125^4

Vì 6561^4 > 3125^4 ⇒3^34 >5^2

\(2^{333}< 3^{222}\)

mình cần cách giải

\(2^{50}=\left(2^5\right)^{10}=32^{10}\)

\(5^{20}=\left(5^2\right)^{10}=25^{10}\)

Suy ra: 2⁵⁰ > 5²⁰

b)

\(9^{200}=\left(9^2\right)^{100}=81^{100}\)

Suy ra: 99¹⁰⁰ > 81¹⁰⁰

\(5^{202}=\left(5^2\right)^{101}=25^{101}\)

\(2^{505}=\left(2^5\right)^{101}=32^{101}\)

Suy ra: 5²⁰² < 2⁵⁰⁵

ko biết

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1,10²⁰và 90¹⁰

ta có:+,10²⁰=(10²)¹⁰=100¹⁰

        +,90¹⁰=90¹⁰

vì 100¹⁰>90¹⁰=>10²⁰>90¹⁰

2,(1/16)¹⁰ và (1/2)⁵⁰

ta có:+, (1/16)¹⁰=(1/16)¹⁰

         +,(1/2)⁵⁰=(1/2⁵)¹⁰=(1/32)¹⁰

vì (1/16)¹⁰>(1/32)¹⁰=>(1/16)¹⁰>(1/2)⁵⁰

k mik nhé

\(a,\)  \(10^{20}=10^{10+10}=10^{10}.10^{10}\)

        \(90^{10}=9^{10}.10^{10}\)

  Vì \(10^{10}.10^{10}>9^{10}.10^{10}\)

    \(\Rightarrow10^{20}>90^{10}\)

Vậy \(10^{20}>90^{10}\)

\(b,\)\(\left(\frac{1}{16}\right)^{10}=\frac{1^{10}}{16^{10}}=\frac{1}{\left(4^2\right)^{10}}=\frac{1}{4^{20}}\)

   \(\left(\frac{1}{2}\right)^{50}=\frac{1^{50}}{2^{50}}=\frac{1}{\left(2^2\right)^{25}}=\frac{1}{4^{25}}\)

Vì \(\frac{1}{4^{20}}>\frac{1}{4^{25}}\)

\(\Rightarrow\left(\frac{1}{16}\right)^{10}>\left(\frac{1}{2}\right)^{50}\)

Vậy \(\left(\frac{1}{16}\right)^{10}>\left(\frac{1}{2}\right)^{50}\)

                         ~~~~~~~~~~Hok tốt~~~~~~~~~~~