Apply the Properties of Integer Exponents to generate equivalent expressions to 40 ⋅ 5−2(−2)−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.

Answer 1

To apply the properties of integer exponents, let's break down the expression step by step:

40 ⋅ 5−2(−2)−3

First, let's simplify the negative exponents:
40 ⋅ 5^(-2) ⋅ (-2)^(-2) ⋅ (-2)^(-3)

Now, let's apply the property of a negative exponent:
40 ⋅ (1/5^2) ⋅ (1/(-2)^2) ⋅ (1/(-2)^3)

Next, let's simplify the exponents:
40 ⋅ (1/25) ⋅ (1/4) ⋅ (1/(-8))

Now, let's multiply the numerators and denominators:
40 ⋅ 1 ⋅ 1 ⋅ 1 / (25 ⋅ 4 ⋅ (-8))

Simplifying further:
40 / (100 ⋅ (-8))

Now, let's multiply the numbers in the denominator:
40 / (-800)

Finally, let's simplify the fraction:
40 / (-800) = -1/20

Therefore, the expression 40 ⋅ 5^(-2)(-2)^(-2)(-2)^(-3) simplifies to -1/20.