Question

Apply the properties of Integer Exponents and find the simplified answer. 4^0 * 5^-2/(-2)^-3

Answer 1

To simplify the given expression (4^0 * 5^(-2))/(-2)^(-3), we can apply the properties of integer exponents:

First, let's simplify each exponent individually.

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

Now, let's simplify the negative exponents.

5^(-2) = 1/(5^2) = 1/25 (A negative exponent indicates the reciprocal of the positive exponent.)

(-2)^(-3) = 1/((-2)^3) = 1/(-2)^3 = 1/(-8) = -1/8 (Again, a negative exponent indicates the reciprocal of the positive exponent.)

Substituting these simplified values into the expression, we have:

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

To divide fractions, we multiply by the reciprocal of the second fraction:

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

Simplifying this multiplication:

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

Therefore, the simplified answer is -8/25.