(Laws of Exponents with Integer Exponents LC) Simplify \( \left(2^{4}\right)^{-1} \) \( \begin{array}{l}-2^{4} \\ \frac{1}{2^{3}} \\ \frac{1}{2^{4}}\end{array} \)

To simplify \( \left(2^{4}\right)^{-1} \), we apply the negative exponent rule, which states that \( a^{-n} = \frac{1}{a^{n}} \). Therefore, \( \left(2^{4}\right)^{-1} = \frac{1}{2^{4}} \). The correct answer is \( \frac{1}{2^{4}} \). Understanding this concept can be a game changer! Many students tend to overlook negative exponents and can confuse them with other properties of exponents. Make sure to remember that a negative exponent signifies the reciprocal of the number raised to the positive exponent. If you're curious about exponents, you might dive into the fascinating world of logarithms next! They are essentially the opposite of exponents and provide a bridge between multiplication and addition. This nifty relationship comes in handy for simplifying complex expressions and solving exponential equations!