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a = -4.

Step-by-step explanation:

25(√5)^a * (√5) ^3  = 5√5

25*5^a/2 * 5^3/2 = 5*5^1/2

25*5^a/2  = 5*5^1/2 / 5^3/2

25*5^a/2  = 5^1 *5^1/2 / 5^3/2

25*5^a/2 = 5^3/2 / 5^3/2 = 1

5^a/2 =  1/25 = 5^-2

The bases are equal, so

a/2 = -2

a = -4.

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