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

1 answer

To simplify this expression, we can follow the order of operations (PEMDAS).

Step 1: Calculate any exponents

4^0 = 1 (Any number raised to the power of 0 is equal to 1).

(-2)^-3 = 1/(-2)^3 = 1/(-2 x -2 x -2) = 1/-8 = -1/8

Step 2: Calculate the division

5^-2 / -1/8 = 5^-2 x -8/1

Step 3: Calculate the multiplication

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

Step 4: Calculate the remaining exponents and multiplication

(-8 x 1)/(5^2 x 1) = -8/25

Therefore, 4^0 x 5^-2 / (-2)^-3 = -8/25.