Question

Which is greater 2^300 or 3^200

Answer 1

SOLUTION

TO DETERMINE

$\sf{The \: greater \: between \: \: \: {2}^{300} \: \: and \: \: {3}^{200} }$

FORMULA TO BE IMPLEMENTED

We are aware of the identity on indices that

$\sf{ {( {a}^{m} )}^{n} = {a}^{mn} \: }$

EVALUATION

Here

$\sf{ {2}^{300} }$

$= \sf{ {( {2}^{3}) }^{100} }$

$= \sf{ {8 }^{100} }$

Again

$\sf{ {3 }^{200} }$

$= \sf{ {( {3}^{2}) }^{100} }$

$= \sf{{9}^{100} }$

Now

$\sf{9 > 8 \: }$

$\implies \sf{ {9}^{100} > {8}^{100} \: }$

$\implies \sf{ {3 }^{200} > {2}^{300} }$

FINAL ANSWER

$\boxed{ \: \sf{ {3 }^{200} > {2}^{300} } \: \: }$

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

The product of two successive multiples of 5 is 300. What are the values of these multiples

https://brainly.in/question/26660243

Answer 2

Answer:

3^200

Step-by-step explanation: