Which expression is equivalent to \( 5^{-6} \times 5^{-5} ? \) Answer \( \begin{array}{ll}5^{30} & 5^{11} \\ 5 & \frac{1}{5^{11}}\end{array} \)

To simplify the expression \( 5^{-6} \times 5^{-5} \), we can use the property of exponents that states \( a^m \times a^n = a^{m+n} \). So, we add the exponents: \(-6 + (-5) = -11\). Thus, the expression simplifies to \( 5^{-11} \), which is equivalent to \( \frac{1}{5^{11}} \). For a bit of math fun, let's remember that negative exponents indicate division. So, if you ever find yourself wrestling with a negative exponent, think of it as doing a little reverse ballet, where you're gracefully pirouetting from the numerator to the denominator! When dealing with expressions involving exponents, a common mistake is to forget to add the exponents together. Always double-check whether you’re adding or multiplying powers of the same base. It’s an easy slip, but it can lead to a tangled web of incorrect calculations!