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 use the following rules:
1. Any number raised to the power of 0 is equal to 1.
2. To divide two numbers with like bases but different exponents, subtract the exponents and keep the base the same.
3. To raise a power to another power, multiply the exponents.

Now, let's apply these properties to simplify the expression:

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

Since 4^0 equals 1, we can rewrite the expression as:

1 * 5^-2 * (-2)^3

Next, we can use the third property to simplify (-2)^3:

1 * 5^-2 * (-2)^3 = 1 * 5^-2 * (-2 * -2 * -2)

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

Now, let's use the second property to rewrite 5^-2:

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

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

Finally, we can multiply the fractions:

= -8/25

Therefore, the simplified fraction for the expression 4^0 * 5^-2 * (-2)^3 with only positive exponents is -8/25.