Apply the Properties of integer exponents to generate an equivalent expression to 4^0x5^(-2)/(-2)^(-3) with only positive exponents, then solve the expression. As a whole number.

Answer 1

To generate an equivalent expression with only positive exponents, we can use the following properties of integer exponents:

1. Property 1: Any non-zero number raised to the power of 0 is equal to 1.
2. Property 2: A negative exponent can be converted to a positive exponent by taking its reciprocal.

Applying these properties, we can rewrite the expression as follows:

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

First, let's simplify the expression inside the parentheses:

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

Now, let's simplify the division:

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

= -(8/25)

So, the equivalent expression is -(8/25).

Since we are looking for the solution as a whole number, we can see that the solution is -8 divided by 25, which gives us -0.32. However, -0.32 is not a whole number.

Therefore, there is no solution to the given expression as a whole number.