Question

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.

Answer 1

To apply the properties of integer exponents, we can rewrite the expression using the following rules:

1. Any number raised to the power of zero is equal to 1: a^0 = 1
2. For any number a, a^(-n) = 1 / a^n (reciprocal)

Applying these rules to the expression 4^0 * 5^-2(-2)^-3, we get:

4^0 * 5^-2(-2)^-3 = 1 * 1 / (5^2 * 1 / (-2)^3)

= 1 / (5^2 * 1 / (-8))

= 1 / (25 * 1 / (-8))

= 1 / (25 / (-8))

= -8/25

Therefore, the answer is -8/25.