Answer:
x = 1/2
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)^c = a^(bc)
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(5^(1/5))^5 = 25^x . . . . given
5^(1/5×5) = (5^2)^x . . . . simplify left side, rewrite right side
5^1 = 5^(2x) . . . . . . . . . simplify further
1 = 2x . . . . . . . . . . . . . equate exponents of the same base
x = 1/2 . . . . . . . . . . . divide by 2
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Additional comment
The Order of Operations tells you that exponentiation must be evaluated before multiplication or division. That means 5^1/5 is evaluated as ...
(5^1)/5 = 5/5 = 1
If you want a fractional exponent, it must be put in parentheses: 5^(1/5). If you type your expression into the Go.ogle calculator, it will strictly adhere to the Order of Operations.
