4^0•5^-2/(-2)^-3
To simplify the given expression:
First, we will work with the exponents. Recall that for any nonzero number a, a^0 = 1.
So, 4^0 becomes 1.
Next, we'll apply the negative exponent rule, which states that a^-n = 1/a^n.
Therefore, 5^-2 becomes 1/5^2 = 1/25.
Finally, we'll simplify the expression by substituting the simplified values:
4^0 • 5^-2 / (-2)^-3 = 1 • 1/25 / (-1/8)
Recall that dividing by a fraction is equivalent to multiplying by its reciprocal:
= 1 • 1/25 • -8/-1
= 1/25 • 8/1
= 8/25