What is 2 Raised to the Power of 100

Answer:

2 raised to the power of 100 can be written in the exponential form as 2¹⁰⁰.

•  According to the Power Law of Exponents, we know a^mn = (a^m)ⁿ. It means that we can simplify the power of a power by multiplying them and then calculating the value with the base as it is, or, a bigger power can be split and the question can be solved further with the base as it is.

So, 2¹⁰⁰ can be expressed as 2 raised to the product of two numbers.

= > 2¹⁰⁰ = 2^10×10 = (2¹⁰)¹⁰

= > 2¹⁰ = 1024

Therefore, (2¹⁰)¹⁰ = (1024)¹⁰

(1024)¹⁰= 1267650600228229401496703205376

Therefore, 2¹⁰⁰ = 1267650600228229401496703205376

This can be expressed in a simpler form.

Hence, 2¹⁰⁰ = 1.2676506002 x 10³⁰

It can also be written as 2¹⁰⁰ = 1.2676506e + 30

• This question can be solved using the logarithm function also.

Let’s suppose, y = 2¹⁰⁰

Taking log on both sides, we obtain

=> log y = log (2¹⁰⁰)

By laws of logarithm function,

=> log y = 100 log (2) [log (x)^m = m log x]

log (2) = 0.69315

=> log y = 100 x 0.69315

=> log y = 69.315

Taking e on both sides,

=> e^logy= e^69.315

Therefore, y = 2¹⁰⁰ = 1.2680081 x 10³⁰ [approx. using value of e]