Which expression is equivalent to \( \frac{6^{-7}}{6} ? \) Answer \( \begin{array}{ll}6^{6} & 6^{-6} \\ 6^{-8} & 6^{7}\end{array} \)

To simplify the expression \( \frac{6^{-7}}{6} \), remember that dividing by a number is the same as multiplying by its reciprocal. In this case, \( \frac{6^{-7}}{6} = 6^{-7} \times 6^{-1} = 6^{-7 - 1} = 6^{-8} \). So, the expression simplifies to \( 6^{-8} \), making that the equivalent expression! Here’s a fun fact: negative exponents are a nifty way to express very small numbers in science and math, like measuring the concentration of certain substances in chemistry! By using negative exponents, scientists can communicate complex information in a compact form. Also, when working with exponents, one common mistake is forgetting the negative sign when combining powers. Always double-check your calculations to ensure you correctly handle any negative exponents!