Question

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.

Answer 1

thats wrong

Answer 2

To apply the Properties of Integer Exponents, we need to understand the following rules:

1) Product Rule: a^m * a^n = a^(m+n)
2) Quotient Rule: a^m / a^n = a^(m-n)
3) Power Rule: (a^m)^n = a^(m*n)
4) Negative Exponent Rule: a^-n = 1 / a^n
5) Zero Exponent Rule: a^0 = 1

Applying these rules, we can rewrite the expression:

4^0 * 5^-2 / (-2)^-3

Using the zero exponent rule for 4^0 and the negative exponent rule for 5^-2 and (-2)^-3, we get:

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

Simplifying further:

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

Multiplying by the reciprocal of the denominator:

1 * (-8 / 1) = -8

Therefore, the expression is equal to -8.

Answer 3

Apologies for the mistake. Let's try again:

To apply the Properties of Integer Exponents, we can simplify the expression:

4^0 * 5^-2 / (-2)^-3

First, let's evaluate the exponents:

4^0 = 1 (any number raised to the power of 0 is equal to 1).

5^-2 = 1 / 5^2 = 1 / 25 (using the negative exponent rule).

(-2)^-3 = 1 / (-2)^3 = 1 / (-8) (using the negative exponent rule).

Now we can substitute these simplified exponents back into the expression:

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

Next, let's simplify the division by multiplying by the reciprocal of the denominator:

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

Now we can multiply the fractions:

(-8) / 25

Thus, the expression is equal to -8/25.