4^0 • 5^-2/(-2)^-3

Answer 1

To solve the expression \( \frac{4^0 \cdot 5^{-2}}{(-2)^{-3}} \), we can simplify it step by step.

1. Simplify \( 4^0 \): \[ 4^0 = 1 \]

2. Simplify \( 5^{-2} \): \[ 5^{-2} = \frac{1}{5^2} = \frac{1}{25} \]

3. Calculate the numerator: \[ 4^0 \cdot 5^{-2} = 1 \cdot \frac{1}{25} = \frac{1}{25} \]

4. Simplify \( (-2)^{-3} \): \[ (-2)^{-3} = \frac{1}{(-2)^3} = \frac{1}{-8} = -\frac{1}{8} \]

5. Now, substitute back into the expression: \[ \frac{\frac{1}{25}}{-\frac{1}{8}} = \frac{1}{25} \cdot \left(-8\right) = -\frac{8}{25} \]

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