apply the properties of integer exponents to generate equivalent expressions to 4^0 • 5^-2/(-2)^-3 with only positive exponents then solve the expression your answer will be a simplified fraction with no remaining exponents
To apply the properties of integer exponents, we can use the following rules:
1. Any non-zero number raised to the power of 0 is equal to 1: x^0 = 1 (where x is any non-zero number)
2. Any number raised to a negative exponent is equal to its reciprocal raised to a positive exponent: x^(-n) = 1 / x^n (where x is any non-zero number)
Using these properties, we can rewrite the expression 4^0 • 5^-2 / (-2)^-3 as follows:
4^0 • 5^-2 / (-2)^-3
= 1 • (1/5^2) / (1/(-2)^3) (Using property 1 and property 2)
= 1 • 1/25 / 1/(-8) (Simplifying exponents)
= 1 • (-8) / 25
= -8/25
Therefore, the simplified fraction of the expression 4^0 • 5^-2 / (-2)^-3 is -8/25.