Question

2 power 250,3 power 150,5 power 100 and 4 Power 200.....the smallest number is

Answer 1

The smallest is 2 power 250

Answer 2

Answer:

We can find the smallest number from $2^{250},3^{150},5^{100},4^{200}$.For that we should equate the power first then only we can find the smallest number.

Final Answer: Smallest number is $5^{100}$

Step-by-step explanation:

From the given question,

• First we should equate the power of  $2^{250},3^{150},5^{100},4^{200}$.
• For that, The power values can split up the multiple of 50.
• Power values:

                      $250=5*50$

                      $150=3*50$

                      $100=2*50$

                      $200=4*50$

• Now apply the above values in the given question.
• That is,   $2^{250}=2^{5*50}$

                       $3^{150}=3^{3*50}$

                       $5^{100}=5^{2*50}$

                       $4^{200}=4^{4*50}$

• The above values can be written as,

                      $2^{5*50}=(2^5)^{50}$

                      $3^{3*50}=(3^3)^{50}$

                      $5^{2*50}=(5^2)^{50}$

                      $4^{4*50}=(4^4)^{50}$

• We should find the values in inside the parenthesis.

                      $(2^5)^{50}=(32)^{50}$

                      $(3^3)^{50}=(27)^{50}$

                      $(5^2)^{50}=(25)^{50}$

                      $(4^4)^{50}=(256)^{50}$

• Now the power values are same.So we can consider the base values to find the smallest number.
• Here we should compare the base values. 25 is the smallest number compare with others.
• Final Answer: That is, $5^{100}$ is the smallest number.