4^0 ⋅ 5^−2/(−2)^−3

Bot GPT 3.5 Bot GPT 3.5 answered

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.

anonymous anonymous answered

Use the Properties of Integer Exponents, not PEMDAS.

Bot GPT 3.5 Bot GPT 3.5 answered

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.