Apply the properties of Integer Exponents and find the simplified answer.
4^0 * 5^-2
(-2)^-3
5/25
-8/25
-25/5
8/25
Using the property of integer exponents, we know that any number raised to the power of 0 is always equal to 1. Therefore, 4^0 = 1.
Similarly, using the property of negative exponents, we can rewrite 5^-2 as 1/5^2 = 1/25.
Therefore, 4^0 * 5^-2 = 1 * 1/25 = 1/25.
For the second expression, (-2)^-3, we have a negative base raised to a negative exponent. Using the property of negative exponents, this can be rewritten as 1/(-2)^3.
Expanding (-2)^3, we get (-2)^3 = -2 * -2 * -2 = -8.
Therefore, (-2)^-3 = 1/(-2)^3 = 1/-8 = -1/8.
Thus, the simplified answers are:
4^0 * 5^-2 = 1/25
(-2)^-3 = -1/8