Multiple Choice 5 points Simplify the expression. \( \frac{m^{-6} n^{-3}}{m^{-13} n^{-1}} \) \( m^{-7} n^{-2} \) \( \frac{m^{-19} n^{-4}}{m^{19} n^{4}} \) \( \frac{m^{7}}{n^{2}} \)

To simplify the expression \( \frac{m^{-6} n^{-3}}{m^{-13} n^{-1}} \), you can use the properties of exponents. When dividing like bases, subtract the exponents: 1. For \( m \): \( -6 - (-13) = -6 + 13 = 7 \) 2. For \( n \): \( -3 - (-1) = -3 + 1 = -2 \) Thus, the simplification results in \( m^{7} n^{-2} \), which can be written as \( \frac{m^{7}}{n^{2}} \). So the correct answer is \( \frac{m^{7}}{n^{2}} \). Now let’s add some engaging information! To better grasp how exponents work, think of them as shorthand for repeated multiplication. For instance, \( m^3 \) means you multiply \( m \) by itself three times: \( m \times m \times m \). This makes simplifying expressions faster than writing all the terms out! When working with exponents, a common mistake is forgetting to apply the negative sign correctly. Remember that a negative exponent indicates a reciprocal. For example, \( m^{-2} \) means \( \frac{1}{m^{2}} \). When you're simplifying, keeping an eye on those negatives can save you from making errors!