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, we can use the following rules:

1. Product of Powers: 𝑎^𝑚 ⋅ 𝑎^𝑛 = 𝑎^(𝑚+𝑛)
2. Quotient of Powers: 𝑎^𝑚 / 𝑎^𝑛 = 𝑎^(𝑚−𝑛)
3. Power of a Power: (𝑎^𝑚)^𝑛 = 𝑎^(𝑚⋅𝑛)
4. Negative Exponent: 𝑎^−𝑚 = 1/𝑎^𝑚

Now let's apply these rules to simplify the expression:

40 ⋅ 5^(-2) * (-2)^(-3)

Using the Negative Exponent rule, we can rewrite 5^(-2) as 1/5^2, and (-2)^(-3) as 1/(-2)^3:

40 ⋅ 1/5^2 * 1/(-2)^3

Simplifying further:

40 ⋅ 1/25 * 1/(-8)

To multiply fractions, we multiply the numerators together and the denominators together:

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

Simplifying the fraction:

40/(-200) = -1/5

Therefore, the simplified fraction is -1/5.

Answer 2

wrong

Answer 3

I apologize for the mistake. Let's try again.

The expression is: 40 * 5^(-2) * (-2)^(-2)^(-3)

Using the Properties of Integer Exponents:

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

Now let's simplify each term:

40 * (1/25) * (1/(2^(-2)^3))

Using the Property of Negative Exponents: (1/(2^(-2)^3)) = 2^(2^3)

40 * (1/25) * 2^(2^3)

Calculating 2^3, we get:

40 * (1/25) * 2^(8)

Now, using the property 2^(2^3) = 2^(8), we have:

40 * (1/25) * 2^(8)

Now, we calculate 2^(8):

40 * (1/25) * 256

Simplifying the multiplication:

(40 * 1 * 256) / 25

= (10240) / 25

Simplifying the quotient:

410.4

Therefore, the expression simplifies to 410.4.