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

Key Concepts

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the absolute value of the exponent. For example, a^-n = 1/a^n. This concept is crucial for rewriting expressions without negative exponents, as it allows us to transform terms into a more standard form that is easier to evaluate.

Reciprocal

The reciprocal of a number is defined as 1 divided by that number. In the context of negative exponents, understanding reciprocals is essential because it allows us to convert expressions like a^-n into 1/a^n. This transformation is fundamental when simplifying expressions and ensuring all exponents are non-negative.

Evaluation of Expressions

Evaluating an expression involves substituting values for variables and performing the necessary arithmetic operations to simplify the expression to a single numerical value. In the case of (-4)^-3, after rewriting it using the negative exponent rule, we can compute the final value, which is important for fully answering the question.