To simplify the expression, we can use the rule of exponents that states that when dividing two numbers with the same base, we subtract the exponents.
(5)^-5 / (5)^7 = 5^(-5 - 7) = 5^-12
Now, we apply the rule that states that a negative exponent is equivalent to the reciprocal of the positive exponent.
5^-12 = 1 / 5^12
So, the simplified expression is 1 / 5^12.
(5)^ -5 (5)^7
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