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.(1 point) 4^0 ⋅ 5^−2/(−2)^−3=

Answer 1

Using the property of integer exponents that states a^0 = 1 for any value of a, we can rewrite 4^0 as 1.

Using the property of negative exponents that states a^-n = 1/a^n for any value of a and n, we can rewrite 5^-2 as 1/5^2 and (-2)^-3 as 1/(-2)^3.

Now the expression becomes:

1 ⋅ 1/(1/5^2) / (1/(-2)^3)

Simplifying further, we can multiply the numerators and denominators:

1 ⋅ (5^2) / (-2)^3

This simplifies to:

25 / -8

Thus, the simplified fraction with no remaining exponents is -25/8.