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Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. P - Fundamental Concepts of AlgebraProblem 16
Chapter 1, Problem 16

Evaluate each exponential expression in Exercises 1–22. (33)2(3^3)^2

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Identify the given expression: \( (3^3)^2 \). This is a power raised to another power.
Recall the exponent rule for powers raised to powers: \( (a^m)^n = a^{m \times n} \).
Apply the rule by multiplying the exponents: \( 3^{3 \times 2} \).
Simplify the exponent multiplication: \( 3^6 \).
Evaluate \( 3^6 \) by multiplying 3 by itself 6 times (if needed, but the problem only asks to express the simplified form).

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Key Concepts

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

Exponents and Powers

Exponents indicate how many times a base number is multiplied by itself. For example, 3^3 means 3 multiplied by itself three times (3 × 3 × 3). Understanding this helps in evaluating expressions involving powers.
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Power of a Power Rule

When an exponent is raised to another exponent, multiply the exponents. For instance, (3^3)^2 equals 3^(3×2) = 3^6. This rule simplifies expressions with nested exponents.
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Evaluating Exponential Expressions

After simplifying the exponents, calculate the numerical value by multiplying the base the required number of times. For example, 3^6 = 3 × 3 × 3 × 3 × 3 × 3 = 729.
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Evaluating Algebraic Expressions
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