To create an equivalent expression from the given situation, let's break down the components step by step.
We start with what appears to be \(0.5^{-2}\) and \((-2)^{-3}\).
-
Handling \(0.5^{-2}\):
- By the properties of exponents, \(a^{-n} = \frac{1}{a^n}\).
- Thus: \[ 0.5^{-2} = \frac{1}{0.5^2} \]
- Calculating \(0.5^2\): \[ 0.5^2 = \frac{1}{4} \]
- Therefore: \[ 0.5^{-2} = \frac{1}{\frac{1}{4}} = 4 \]
-
Handling \((-2)^{-3}\):
- Again using the property of exponents: \[ (-2)^{-3} = \frac{1}{(-2)^3} \]
- Calculating \((-2)^3\): \[ (-2)^3 = -8 \]
- Therefore: \[ (-2)^{-3} = \frac{1}{-8} \]
Now, substitute back:
We have the expression composed of:
\[ \frac{0.5^{-2}}{(-2)^{-3}} = \frac{4}{\frac{1}{-8}} \]
- Calculating the final expression:
- Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{4}{\frac{1}{-8}} = 4 \times -8 = -32 \]
Therefore, the final simplified answer is:
\[ \boxed{-32} \]