2) \( \left(\frac{1}{4}\right)^{-2} \)

To evaluate the expression \( \left(\frac{1}{4}\right)^{-2} \), let's break it down step by step using the rules of exponents. ### Step 1: Understand Negative Exponents A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. In general: \[ a^{-n} = \frac{1}{a^n} \] So, \[ \left(\frac{1}{4}\right)^{-2} = \frac{1}{\left(\frac{1}{4}\right)^2} \] ### Step 2: Calculate the Positive Exponent First, compute \( \left(\frac{1}{4}\right)^2 \): \[ \left(\frac{1}{4}\right)^2 = \frac{1^2}{4^2} = \frac{1}{16} \] ### Step 3: Take the Reciprocal Now, take the reciprocal of \( \frac{1}{16} \): \[ \frac{1}{\left(\frac{1}{4}\right)^2} = \frac{1}{\frac{1}{16}} = 16 \] ### Final Answer \[ \left(\frac{1}{4}\right)^{-2} = 16 \]