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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 47
Chapter 1, Problem 47

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

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Recall the rule for negative exponents: for any nonzero number \(a\) and integer \(n\), \(a^{-n} = \frac{1}{a^n}\). This means a negative exponent indicates the reciprocal of the base raised to the positive exponent.
Apply this rule to the expression \(-a^{-3}\). The negative exponent on \(a\) means we rewrite \(a^{-3}\) as \(\frac{1}{a^3}\).
Rewrite the entire expression by replacing \(a^{-3}\) with \(\frac{1}{a^3}\), so the expression becomes \(-\frac{1}{a^3}\).
Since the expression now has no negative exponents, it is written without negative exponents as required.
Evaluate the expression only if a specific value for \(a\) is given; otherwise, this is the simplified form assuming \(a \neq 0\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. For example, a⁻³ equals 1 divided by a³. Understanding this allows rewriting expressions without negative exponents by moving factors between numerator and denominator.
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Exponent Rules

Exponent rules govern how to manipulate powers, including product, quotient, and power of a power rules. These rules help simplify expressions and rewrite them in equivalent forms, essential for removing negative exponents and evaluating expressions correctly.
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Evaluating Expressions with Variables

When variables represent nonzero real numbers, expressions can be simplified but not numerically evaluated without specific values. Recognizing this helps in simplifying expressions correctly and understanding when evaluation is possible or not.
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