Write each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. 4x^-2

Verified step by step guidance

1. Recall the rule for negative exponents: \(a^{-n} = \frac{1}{a^n}\), where \(a \neq 0\) and \(n\) is a positive integer.
2. Apply this rule to the expression \$4x^{-2}\(. Rewrite \)x^{-2}\( as \)\frac{1}{x^2}\(, so the expression becomes \)4 \cdot \frac{1}{x^2}$.
3. Simplify the expression by multiplying the constants and variables: \(\frac{4}{x^2}\).
4. Since the problem states to evaluate if possible and all variables represent nonzero real numbers, check if any further simplification or numerical evaluation is possible. Here, no numerical value is given for \(x\), so the expression remains \(\frac{4}{x^2}\).
5. The final expression without negative exponents is \(\frac{4}{x^2}\).

Key Concepts

Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. For example, x^-n equals 1 divided by x^n. This rule helps rewrite expressions without negative exponents by converting them into fractions.

Exponent Rules

Exponent rules govern how to manipulate powers, including product, quotient, and power of a power rules. Understanding these rules allows simplification and evaluation of expressions involving exponents, ensuring correct handling of variables and constants.

Evaluating Expressions with Variables

When variables are involved, expressions can be simplified symbolically unless specific values are given. Assuming variables are nonzero avoids division by zero errors, enabling safe manipulation of expressions with negative exponents.