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. Identify the expression with the negative exponent: $4x^{-2}$.
2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$.
3. Apply the rule to the expression: $4x^{-2} = 4 \cdot \frac{1}{x^2}$.
4. Rewrite the expression: $\frac{4}{x^2}$.
5. The expression is now written without negative exponents.

Key Concepts

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the absolute value of the exponent. For example, x^-n can be rewritten as 1/x^n. Understanding this concept is crucial for rewriting expressions without negative exponents, as it allows for simplification and clearer representation of mathematical expressions.

Simplifying Expressions

Simplifying expressions involves rewriting them in a more manageable or standard form. This process often includes combining like terms, reducing fractions, and eliminating negative exponents. Mastery of simplification techniques is essential for evaluating expressions accurately and efficiently.

Evaluating Expressions

Evaluating expressions means substituting values for variables and performing the necessary arithmetic operations to find a numerical result. In the context of the given expression, it is important to first rewrite it without negative exponents before substituting any values. This ensures that the evaluation is done correctly and adheres to mathematical conventions.