Question

Apply the properties of Integer Exponents and find the simplified answer.

4^0 * 5^-2
(-2)^-3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify these expressions, we can apply the following properties of integer exponents:

1. For any non-zero number a, a^0 = 1.
2. For any non-zero number a, a^(-n) = 1/a^n.

Using these properties, let's simplify the given expressions:

1. 4^0 * 5^-2:
Using property 1, we know that any number raised to the power of 0 is equal to 1. So, 4^0 = 1.
Using property 2, we know that 5^-2 = 1 / 5^2 = 1/25.
Therefore, 4^0 * 5^-2 = 1 * 1/25 = 1/25.

2. (-2)^-3:
Using property 2, we know that (-2)^-3 = 1 / (-2)^3 = 1 / (-2 * -2 * -2) = 1 / (-8) = -1/8.

Therefore, the simplified answers are:
1. 4^0 * 5^-2 = 1/25.
2. (-2)^-3 = -1/8.