Question

Apply All Exponent Rules Practice
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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.(1 point)
4^0 ⋅ 5^−2/(−2)^−3=

Answer 1

To simplify the given expression \( \frac{4^0 \cdot 5^{-2}}{(-2)^{-3}} \) using the properties of integer exponents, follow these steps:

1. **Simplify \(4^0\)**: Any non-zero number raised to the power of 0 is 1. Thus, \(4^0 = 1\).

\[
\frac{1 \cdot 5^{-2}}{(-2)^{-3}}
\]

2. **Rewrite \(5^{-2}\)**: According to the negative exponent rule, \(a^{-n} = \frac{1}{a^n}\). So,

\[
5^{-2} = \frac{1}{5^2} = \frac{1}{25}
\]

Now we can update our expression:

\[
\frac{1/25}{(-2)^{-3}}
\]

3. **Rewrite \((-2)^{-3}\)**: Similarly,

\[
(-2)^{-3} = \frac{1}{(-2)^3} = \frac{1}{-8}
\]

Now we can rewrite the expression:

\[
\frac{1/25}{1/(-8)} = \frac{1}{25} \cdot \frac{-8}{1} = \frac{-8}{25}
\]

4. **Final simplified result**:

\[
\frac{-8}{25}
\]

Thus, the final answer is:

\[
\frac{-8}{25}
\]