Apply the properties of integer exponents to generate equivalent expressions that is four when the power of 0×5 with the power of -2 over and parentheses -2 when the power of -3 with only positive exponents then solve the expression your answer will be a simplified fraction with no remaining exponents

1 answer

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 \((-2)^{-3}\).

  1. 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: \[ 0.5^{-2} = \frac{1}{\frac{1}{4}} = 4 \]
  2. 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:

\[ \frac{0.5^{-2}}{(-2)^{-3}} = \frac{4}{\frac{1}{-8}} \]

  1. 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:

\[ \boxed{-32} \]