Question

Apply the Properties of Integer Exponents to generate equivalent expressions to 4 to the power of 0 ⋅ 5 to the power of −2/(−2) to the power of −3
with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
40 ⋅ 5−2(−2)−3=

Answer 1

To simplify the expression \( 4^0 \cdot 5^{-2} / (-2)^{-3} \) using the properties of integer exponents, we can break it down step by step.

1. **Evaluate the individual components:**
- \( 4^0 = 1 \) (any non-zero number raised to the zero power is 1)
- \( 5^{-2} = \frac{1}{5^2} = \frac{1}{25} \)
- \( (-2)^{-3} = \frac{1}{(-2)^3} = \frac{1}{-8} = -\frac{1}{8} \)

2. **Combine the expressions:**
\[
4^0 \cdot 5^{-2} = 1 \cdot \frac{1}{25} = \frac{1}{25}
\]
Now we rewrite the original expression:
\[
\frac{\frac{1}{25}}{-\frac{1}{8}}
\]

3. **Dividing fractions:**
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{1}{25} \cdot -8 = -\frac{8}{25}
\]

Thus, the final answer is:
\[
-\frac{8}{25}
\]