9514 1404 393
Answer:
y = 1
Step-by-step explanation:
Recognize that 25 and 125 are powers of 5 and rewrite the equation in terms of powers of 5.
The applicable rules of exponents are ...
(a^b)^c = a^(bc)
(a^b)/(a^c) = a^(b-c)
(a^b)(a^c) = a^(b+c)
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Your equation can be written as ...
[tex]25^4\div5^{5y}=125^y\\\\(5^2)^4\div5^{5y}=(5^3)^y\\\\5^{8-5y}=5^{3y}\\\\8-5y=3y\qquad\text{equate exponents of the same base}[/tex]
Now this can be solved as an ordinary linear equation.
8 = 8y . . . . . . add 5y to both sides
1 = y . . . . . . . divide by 8
The solution is y = 1.
