Question 98535
{{{(x^5)^10=10^100}}} Start with the given equation


{{{x^50 = 10^100}}} Distribute and multiply the exponents.



{{{root(50,x^50) = root(50,10^100)}}} Take the 50th root (it's like the square root) of both sides



{{{x = root(50,10^100)}}} The left side is now x


{{{x = (10^100)^(1/50)}}} Rewrite {{{root(50,10^100)}}} as {{{(10^100)^(1/50)}}}



Distribute and multiply the exponents. Remember, when taking the even root (such as a square root) there is a positive and negative answer

{{{x = (10)^(100/50)}}} or {{{x = -(10)^(100/50)}}}



{{{x = 10^2}}} or {{{x = -10^2}}} Reduce



{{{x = 100}}} or {{{x=-100}}} Square 10 to get 100


So the answers are {{{x = 100}}} or {{{x=-100}}}