If googol = (x^5)^10, then what is the value of x?

Question

Show your work,

Answer 1

1 googol = 10^100 by definition.

(x^5)^10 = 10^100
x^50 = 10^100
x = ±10² = ±100

Answer 2

Then googol = x^(5*10)
googol = x^50

Assume googol = 10^100

10^100 = x^50
Take 50th root of each side
10^(100/50) = x
x = 10^2 = 100

Answer 3

(x^5)^10 is equal to x^(5*10) = x^50

Googol = 10^100 (source: Wikipedia)

Therefore, if x^50 = 10^100, then x = (10^100)^(1/50) = 10^2 = 100

Answer: x = 100