To apply the properties of integer exponents, we'll use the following rules:
1. Any non-zero number to the power of 0 is equal to 1.
2. When dividing two numbers with the same base and different exponents, subtract the exponents.
3. The reciprocal of a number to a positive exponent is the same as the number to the negative exponent.
Using these rules, we can simplify the expression:
4^0 ⋅ 5^(-2) ⋅ (-2)^(-3)
Using rule 1, 4^0 is equal to 1. So we're left with:
1 ⋅ 5^(-2) ⋅ (-2)^(-3)
Let's simplify 5^(-2) and (-2)^(-3):
5^(-2) = 1/(5^2) = 1/25
(-2)^(-3) = 1/((-2)^3) = 1/(-8) = -1/8
Now we can substitute these simplified values back into the expression:
1 ⋅ 1/25 ⋅ -1/8
Multiplying these fractions, we get:
(-1)/(25 * 8) = (-1)/200
Therefore, the simplified expression is -1/200.