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: $$\frac{\frac{1}{25}}{-\frac{1}{8}}=\frac{1}{25}\cdot (-8)=-\frac{8}{25}$$

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