Question

.
Among the numbers 2^250, 3^200, 4^150,5^100 the greatest number is
O 2^250
O 3^200
4^130
5^100
​

Answer 1

Answer:

3^200

Step-by-step explanation:

2^250=(2^5)^50=32^50

3^200=(3^4)^50=81^50

4^150=(4^3)^50=64^50

5^100=(5^2)^50=25^50

Therefore, 3^200 is the greatest

Answer 2

$\sf The \: greatest \: number \: is \: \: {3}^{200}$

Given :

$\sf The \: numbers \: \: {2}^{250} , {3}^{200}, {4}^{150}, {5}^{100}$

To find :

The greatest number is

$\sf {2}^{250}$

$\sf {3}^{200}$

$\sf {4}^{150}$

$\sf {5}^{100}$

Solution :

Step 1 of 3 :

Write down the given numbers

$\sf The \: numbers \:are \: \: {2}^{250} , {3}^{200}, {4}^{150}, {5}^{100}$

Step 2 of 3 :

Rewrite the numbers with same power

$\sf {2}^{250} = {2}^{(5 \times 50)} = {( {2}^{5} )}^{50} = {32}^{50}$

$\sf {3}^{200} = {3}^{(4 \times 50)} = {( {3}^{4} )}^{50} = {81}^{50}$

$\sf {4}^{150} = {4}^{(3 \times 50)} = {( {4}^{3} )}^{50} = {64}^{50}$

$\sf {5}^{100} = {5}^{(2 \times 50)} = {( {5}^{2} )}^{50} = {25}^{50}$

Step 3 of 3 :

Find the greatest number

$\sf 81 > 64 > 32 > 25$

$\displaystyle \sf{ \implies {81}^{50} >{64}^{50} > {32}^{50} > {25}^{50} }$

$\displaystyle \sf{ \implies {3}^{200} >{4}^{150} > {2}^{250} > {5}^{100} }$

$\sf The \: greatest \: number \: is \: \: {3}^{200}$

Hence the correct option is $\sf {3}^{200}$