Simplify each expression. (a8)(a5)(a)

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 14

Chapter 1, Problem 14

Simplify each expression. (a⁸)(a⁵)(a)

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Identify the base and the exponents in the expression \((a^{8})(a^{5})(a)\). Here, the base is \(a\) for all terms.

Recall the exponent rule for multiplying powers with the same base: \(a^{m} \times a^{n} = a^{m+n}\).

Apply the rule by adding the exponents of each term: \(8 + 5 + 1\) (note that \(a\) is the same as \(a^{1}\)).

Write the simplified expression as \(a^{8+5+1}\).

Combine the exponents by performing the addition inside the exponent to get the final simplified form \(a^{14}\) (do not calculate the final value, just show the step).

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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 of the same base. For multiplication, the exponents are added together, such as a^m * a^n = a^(m+n). This rule allows combining terms with the same base efficiently.

Base Consistency in Exponentiation

When simplifying expressions with exponents, it is essential that the bases are the same to apply exponent rules. In the given expression, all terms have the base 'a', enabling the use of exponent addition to simplify the product.

Simplification of Algebraic Expressions

Simplification involves rewriting expressions in a more compact or standard form without changing their value. Here, combining like terms with exponents reduces the expression to a single power of 'a', making it easier to interpret and use.

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