Question

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.(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To apply the properties of integer exponents, we can rewrite the expression as:

40 * 5^(-2) * (-2)^(-2) * (-2)^(-3)

Using the property that a^(-n) = 1/a^n, we can rewrite the expression again as:

40 * 1/5^2 * 1/(-2)^2 * 1/(-2)^3

Simplifying further, we have:

40 * 1/25 * 1/4 * 1/(-8)

Multiplying all the terms together, we get:

(40 * 1 * 1 * 1) / (25 * 4 * -8)

Simplifying the numerator, we have:

40

And simplifying the denominator, we have:

25 * 4 * -8 = -800

Therefore, the expression simplifies to:

40 / -800

Which can be further simplified as:

-1/20