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

To apply the properties of integer exponents, we need to remember the following rules:

1. 𝑥^𝑛 ÷ 𝑥^𝑚 = 𝑥^(𝑛−𝑚)
2. 𝑥^−𝑛 = 1/𝑥^𝑛
3. 𝑥^0 = 1

Now let's apply these rules to the expression 40 ⋅ 5^−2(−2)^−3:

40 ⋅ 5^(-2)⋅(−2)^(-3)

Using rule 2, we can convert the negative exponents to positive exponents:

40 ⋅ 1/5^2 ⋅ 1/(−2)^3

Using rule 3, we can simplify the expressions with exponent 0:

40 ⋅ 1/(5^2) ⋅ 1/(−2)^3

Now we can simplify the expressions with exponent 2 and 3:

40 ⋅ 1/25 ⋅ 1/(-8)

Also, we can change the division by -8 into multiplication by -1/8:

40 ⋅ 1/25 ⋅ (-1/8)

Now we can simplify this expression:

40 ⋅ (-1/25) ⋅ (-1/8) = -40/25 ⋅ 1/8 = -320/200 = -8/5

So the simplified fraction with no remaining exponents is -8/5.

Answer 2

wrong