Answer:
x = 5^6
Explanation:
We can solve for x by taking the fifth root of both sides of the equation.
(5x)^5 = 5^35
Taking the fifth root of both sides, we get:
5x = 5^(35/5)
5x = 5^7
Now we can solve for x by dividing both sides by 5:
x = 5^7 / 5
x = 5^6
Therefore, the value of x in the equation (5x)^5 = 5^35 is x = 5^6.
To check our answer, we can substitute x = 5^6 into the original equation:
(5x)^5 = 5^35
(5(5^6))^5 = 5^35
(5^7)^5 = 5^35
5^(7x5) = 5^35
5^35 = 5^35
The equation is true, so x = 5^6 is the correct value.