Domanda del libro di testo
Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers.
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 1, Problema 16
Evaluate each exponential expression in Exercises 1–22.
Guida verificata passo dopo passo1
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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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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04:10
Powers of i
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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04:10Powers of i
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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03:11Evaluating Algebraic Expressions
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