Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:26 minutes

Problem 37

Textbook Question

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

Verified step by step guidance

Identify the expression with the negative exponent: \((-4)^{-3}\).

Recall the rule for negative exponents: \(a^{-n} = \frac{1}{a^n}\).

Apply the rule to the expression: \((-4)^{-3} = \frac{1}{(-4)^3}\).

Calculate \((-4)^3\) by multiplying \(-4\) by itself three times: \((-4) \times (-4) \times (-4)\).

Express the result as a fraction: \(\frac{1}{(-4)^3}\).

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Key Concepts

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

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.