Question

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) 40 ⋅ 5−2(−2)−3=

Answer 1

To apply the properties of integer exponents and generate equivalent expressions with only positive exponents, we can use the following rules:

1. For any non-zero number x, x^(-n) = 1/x^n.
2. For any non-zero number x, x^0 = 1.
3. For any non-zero numbers a and b, a^n * b^n = (a * b)^n.

Using these rules, let's simplify the expression:

40 ⋅ 5^(-2)(-2)^(-3)

Using rule 1 for 5^(-2), we have:

40 ⋅ (1/5^2)(-2)^(-3)

Simplifying 5^2 = 25:

40 ⋅ (1/25)(-2)^(-3)

Using rule 2 for (-2)^(-3), we have:

40 ⋅ (1/25)(1/(-2)^3)

Simplifying (-2)^3 = -8:

40 ⋅ (1/25)(1/(-8))

Simplifying 1/(-8):

40 ⋅ (1/25)(-1/8)

Using rule 3 for (1/25)(-1/8), we have:

(40 * 1 * -1) / (25 * 8) = -40 / 200

Simplifying the fraction:

-40 / 200 = -1 / 5

Therefore, the solution is -1 / 5.