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------------------------------------------------ Use the like-bases property and exponents to solve the equation:

\[ 625^{n} = 3125 \]

Answer :

Final answer:

The equation 625^n = 3125 can be solved by recognizing both numbers as powers of 5 and using the like-bases property of exponents to equate the exponents. The value of n is 1.25.

Explanation:

To solve the equation 625n = 3125 using the like-bases property and exponents, it helps to recognize that both 625 and 3125 are powers of 5. Specifically, 625 = 54 and 3125 = 55. So our equation can be rewritten as (54)n = 55. According to the rules of exponents, (ab)c = ab*c. Therefore, 54n = 55. By the like-bases property, we can equate the exponents, giving us 4n = 5. Solving for n gives us n = 5/4 = 1.25.

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