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Let's break down the concept of negative exponents. Understanding this is crucial for simplifying expressions like the ones in the exercise. A negative exponent means you're dealing with a reciprocal. For example, if you have a number with a negative exponent such as \(5^{-1}\), it can be rewritten as \(\frac{1}{5}\). In general, for any non-zero number \(a\) and a positive integer \(n\), \(a^{-n} = \frac{1}{a^n}\). This means you're flipping the fraction. The negative exponent tells you to take the reciprocal and then apply the exponent. For instance, \(2^{-3} = \frac{1}{2^3} = \frac{1}{8}\).

Multiplication is a fundamental arithmetic operation that you'll frequently use when simplifying expressions, especially those involving exponents and fractions. When you multiply numbers, you're adding a number to itself a certain number of times. For example, \(2 \cdot 3\) means 2 added to itself 3 times, or \(2 + 2 + 2 = 6\). Multiplication with fractions follows the same rules, but you multiply the numerators (top numbers) and the denominators (bottom numbers) separately. For example, \(\frac{2}{3} \cdot \frac{4}{5} = \frac{2 \cdot 4}{3 \cdot 5} = \frac{8}{15}\). When dealing with negative exponents in multiplication, you must first convert them into fractions or their reciprocal form before proceeding with the multiplication.

Fractions represent a part of a whole and are written as one number over another, separated by a line. The number on top is called the numerator, and the number at the bottom is called the denominator. For instance, in the fraction \(\frac{3}{4}\), 3 is the numerator, and 4 is the denominator. Fractions are particularly important when working with negative exponents, as we've seen with \(5^{-1} = \frac{1}{5}\). When multiplying fractions, you handle the numerators and denominators separately. For example, multiplying \(2 \cdot \frac{1}{5}\), you can look at it as \(\frac{2}{1} \cdot \frac{1}{5} = \frac{2 \cdot 1}{1 \cdot 5} = \frac{2}{5}\). Understanding how to manipulate fractions accurately is key to simplifying many algebraic expressions.