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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 63
Chapter 1, Problem 63

Simplify each expression. Write answers without negative exponents. Assume all variables represent nonzero real numbers. (5a-1)4(a2)-3

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Start by rewriting the expression clearly: \(\left(5a^{-1}\right)^4 \left(a^2\right)^{-3}\).
Apply the power of a power rule, which states that \((x^m)^n = x^{m \cdot n}\), to each part separately: \(5^4 \cdot (a^{-1})^4 \cdot a^{2 \cdot (-3)}\).
Simplify the exponents: \(5^4 \cdot a^{-4} \cdot a^{-6}\).
Combine the terms with the same base \(a\) by adding their exponents: \(a^{-4 + (-6)} = a^{-10}\).
Rewrite the expression without negative exponents by using the rule \(x^{-m} = \frac{1}{x^m}\), resulting in \(5^4 \cdot \frac{1}{a^{10}}\).

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Key Concepts

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

Laws of Exponents

The laws of exponents govern how to simplify expressions involving powers, such as multiplying powers with the same base by adding exponents, raising a power to another power by multiplying exponents, and handling negative exponents by rewriting them as reciprocals.
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Rational Exponents

Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. For example, a⁻¹ equals 1/a. Simplifying expressions often involves rewriting negative exponents as positive by moving factors between numerator and denominator.
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Zero and Negative Rules

Simplification of Algebraic Expressions

Simplification involves combining like terms and applying exponent rules to write expressions in their simplest form. This includes eliminating negative exponents, reducing powers, and ensuring the final answer is clear and concise, as required in algebra problems.
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Introduction to Algebraic Expressions
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