(5^-2/5^-1)^-4? A. 5^-12. B. 5^-8. C. 5^4. D. 5^-5
To simplify this expression, we can combine the exponents inside the parentheses.
The expression inside the parentheses is (5^-2)/(5^-1). When dividing two numbers with the same base, we subtract the exponents, so this simplifies to 5^(-2 - (-1)) = 5^(-2 + 1) = 5^-1.
Now we have (5^-1)^-4. When raising a number to a negative exponent, we take the reciprocal of the number and make the exponent positive. Therefore, (5^-1)^-4 = (1/5)^-4 = (1/5^4) = 1/625 = 5^-4.
So the simplified expression is 5^-4.
The correct answer is B. 5^-8.