Write each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. -a^-3

Verified step by step guidance

1. Start with the expression: \(-a^{-3}\).
2. Recall that a negative exponent indicates the reciprocal of the base raised to the positive exponent. Therefore, \(a^{-3} = \frac{1}{a^3}\).
3. Apply this rule to the expression: \(-a^{-3} = -\frac{1}{a^3}\).
4. The expression is now written without negative exponents: \(-\frac{1}{a^3}\).
5. Since the problem does not provide a specific value for \(a\), the expression cannot be evaluated further without additional information.

Key Concepts

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the absolute value of the exponent. For example, a^-n can be rewritten as 1/a^n. This concept is crucial for simplifying expressions that contain negative exponents, allowing for easier evaluation and manipulation of algebraic expressions.

Simplifying Expressions

Simplifying expressions involves rewriting them in a more manageable form, often by combining like terms, reducing fractions, or eliminating negative exponents. This process is essential for making calculations easier and clearer, especially when evaluating expressions or solving equations.

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 requires understanding how to handle the rewritten form after removing negative exponents, ensuring that all operations follow the correct order of operations.