Apply the Properties of Integer Exponents to generate equivalent expressions to 4^0 ⋅ 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

Given expression: 4^0 ⋅ 5^−2/(−2)^−3

Using the property a^0 = 1 for any number a, we can rewrite 4^0 as 1:

1 ⋅ 5^−2/(−2)^−3

Using the property (a^m)^n = a^(m*n), we can multiply the exponents of 5 and -2:

1 ⋅ (5^2)/(−2)^−3

Now, using the property a^(-m) = 1/(a^m), we can change the sign of the negative exponent:

1 ⋅ (5^2)/(1/(−2^3))

Simplifying, we have:

5^2/(-2^3)

Since 5^2 = 25 and (-2^3) = -8, the expression becomes:

25/(-8)

This can be simplified further by dividing both the numerator and the denominator by the greatest common divisor (GCD) of 25 and -8, which is 1:

25/(-8)

Therefore, the simplified fraction with no remaining exponents is -25/8.

Answer 2

wrong

Answer 3

Apologies for the mistake.

Let's break down the expression and apply the properties of integer exponents step by step:

1. 4^0 = 1 (any number raised to the power of 0 is equal to 1)
2. 5^-2 = 1/5^2 = 1/25 (applying the property a^-n = 1/a^n)
3. (-2)^-3 = 1/(-2)^3 = 1/(-8) (applying the property a^-n = 1/a^n)

Now, substituting these values back into the original expression, we get:

1 * (1/25) / (1/(-8))

To divide fractions, we can multiply the numerator by the reciprocal of the denominator:

1 * (1/25) * (-8/1)

Simplifying further:

-8/25

Therefore, the equivalent expression with only positive exponents is -8/25.