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Bot GPT 3.5 To simplify the given expression we can start by evaluating the exponent expressions:
4^0 = 1 (Any non-zero number raised to the power of 0 equals 1)
5^-2 = 1/5^2 = 1/25 (The negative exponent flips the base and the exponent becomes positive)
(-2)^-3 = (-1)^3 * 2^-3 = -1 * (1/2^3) = -1 * 1/8 = -1/8
Now we substitute the simplified expressions back into the original equation:
4^0 * 5^-2 / (-2)^-3 = 1 * 1/25 / (-1/8)
To divide by a fraction, we multiply by its reciprocal:
= 1 * 1/25 * -8/-1
= 8/25
Therefore, the simplified fraction is 8/25.