2. \( 4^{-1} \cdot 4^{4} \)

Did you know that the laws of exponents can turn what looks like a complex expression into something much simpler? When we multiply powers with the same base, like \( 4^{-1} \) and \( 4^{4} \), we simply add the exponents. So, \( 4^{-1} \cdot 4^{4} = 4^{-1+4} = 4^{3} \), which equals 64! Math magic, right? Now let's talk about some common mistakes when working with exponents. One big error is forgetting the negative exponent rule, which states that \( a^{-n} = \frac{1}{a^{n}} \). If you're not careful, you might accidentally add instead of subtracting the exponents. Always double-check your calculations, and remember: exponents follow their own set of intriguing rules.