Questions: Simplify the following expression. Write the answer as a reduced fraction. 4^-2=

Solution Steps

To simplify the expression \(4^{-2}\), we need to understand that a negative exponent indicates the reciprocal of the base raised to the positive of that exponent. Therefore, \(4^{-2}\) is equivalent to \(\frac{1}{4^2}\). We then calculate \(4^2\) and take the reciprocal to get the final answer.

We start with the expression \(4^{-2}\). A negative exponent indicates that we take the reciprocal of the base raised to the positive exponent. Thus, we can rewrite the expression as: \[ 4^{-2} = \frac{1}{4^2} \]

Next, we calculate \(4^2\): \[ 4^2 = 16 \]

Now, substituting back into our expression, we have: \[ 4^{-2} = \frac{1}{16} \]

Final Answer