Question

4^0 ⋅ 5^−2/(−2)^−3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression, we can follow the order of operations (PEMDAS/BODMAS).

First, let's simplify the power of 4^0. Any number (except 0) raised to the power of 0 is equal to 1. So, 4^0 = 1.

Next, let's simplify the power of 5^-2. The negative exponent flips the base to the denominator. So, 5^-2 = 1/5^2.
Therefore, 5^-2 = 1/25.

Next, let's simplify (-2)^-3. Again, the negative exponent flips the base to the denominator. So, (-2)^-3 = 1/(-2)^3.
Therefore, (-2)^-3 = 1/(-2^3) = 1/(-8) = -1/8.

Finally, let's substitute these values into the original expression:
4^0 ⋅ 5^-2 / (-2)^-3 = 1 ⋅ 1/25 / -1/8.

Next, we can simplify the division by multiplying the fractions:
(1/1) * (1/25) * (8/-1).

Multiplying the numerators, we have 1 * 1 * 8 = 8.
Multiplying the denominators, we have 1 * 25 * 1 = 25.

So, the expression simplifies to:
8/25.

Answer 2

Use the Properties of Integer Exponents, not PEMDAS.

Answer 3

[AI-generated answer — Bot GPT 3.5]

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

4^0 ⋅ 5^-2 / (-2)^-3

Using the property of any number raised to the power of 0 equaling 1, we have:

1 ⋅ 5^-2 / (-2)^-3

Using the property of a negative exponent, we can write:

1 ⋅ 1/5^2 / 1/(-2)^3

Simplifying further, we have:

1 ⋅ 1/25 / 1/(-8)

Next, dividing by a fraction is the same as multiplying by its reciprocal, so:

1 ⋅ 1/25 * (-8)/1

Multiplying the numerators, we get:

-8/25

Therefore, the simplified expression is -8/25.