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Fractions are a way of representing numbers that are not whole, often called rational numbers. In a fraction, there are two parts: the numerator, which is the top number, and the denominator, which is the bottom number. For example, in the fraction \(-\frac{2}{3}\), - the numerator is \(-2\), and - the denominator is \(3\).Fractions can represent parts of whole objects or values. Here, the fraction \(-\frac{2}{3}\) tells us that we are dealing with \(-2\) parts of something that is divided into \(3\) equal parts.When fractions are squared, both the numerator and the denominator are squared separately. Consider squaring \(-\frac{2}{3}\). You square the numerator, \((-2)^2\), which equals \(4\), and you square the denominator, \((3)^2\), which equals \(9\). Thus, \(\left(-\frac{2}{3}\right)^2 = \frac{4}{9}\). Understanding fractions and their operations is a crucial part of prealgebra and various other math concepts.

Exponents are used in mathematics to express repeated multiplication of a number by itself. The expression \(e^2\) means \(e\) multiplied by itself, i.e., \(e \times e\). For instance, if you have \(e = -\frac{2}{3}\), then \(e^2\) becomes \(\left(-\frac{2}{3}\right) \times \left(-\frac{2}{3}\right)\). The process of finding this involves

• multiplying the numerators and denominators separately, which results in a new fraction.
• In our example, (-2) becomes \(4\) because (-2) times (-2) is positive 4, and (3) times (3) is 9, producing \(\frac{4}{9}\).

A vital property of exponents in prealgebra is that any real number's square is positive, which simplifies handling negative numbers. Thus, understanding exponents helps in solving equations involving power terms effectively.

Negative numbers represent values less than zero and are typically written with a minus sign \(-\) in front of them. They have unique properties in algebra, especially when involved with operations like division or multiplication.When we talk about evaluating expressions such as \(-e^2\) where \(e = -\frac{2}{3}\), negative numbers play an important role. For instance:

• Squaring a negative number results in a positive number. This is because (- times -) equals a positive, as seen in \((-\frac{2}{3})^2 = \frac{4}{9}\).
• However, if you place a negative sign outside an expression you've squared, it switches the final result back to negative as shown in \(-\left(\frac{4}{9}\right) = -\frac{4}{9}\).

Negative numbers can appear in many mathematical contexts beyond just this problem. Being confident in working with them is pivotal for mastering prealgebra concepts and solving more complex algebraic equations.