Textbook Question
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The distance on a number line from a number to 0 is the _________ of the number.
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 1, Problem R.3.15
Simplify each expression. See Example 1. 9³ • 9⁵
Verified step by step guidance1
Recognize that the expression involves multiplication of powers with the same base: \(9^3 \cdot 9^5\).
Recall the exponent rule for multiplying powers with the same base: \(a^m \cdot a^n = a^{m+n}\).
Apply this rule by adding the exponents: \(9^{3+5}\).
Simplify the exponent sum: \$9^8$.
Express the simplified form as \$9^8$, which is the product of the original expression.
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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. Specifically, when multiplying powers with the same base, you add their exponents. For example, a^m * a^n = a^(m+n). This rule is essential for simplifying expressions like 9³ • 9⁵.
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Intro to Law of Cosines
Base and Exponent
In an expression like 9³, 9 is the base and 3 is the exponent, indicating how many times the base is multiplied by itself. Understanding the roles of base and exponent helps in applying exponent rules correctly during simplification.
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4:28Introduction to Inverse Trig Functions
Simplification of Exponential Expressions
Simplification involves rewriting expressions in a simpler or more compact form without changing their value. For exponential expressions, this often means combining like terms using exponent rules to reduce complexity and make calculations easier.
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6:36Simplifying Trig Expressions
Related Practice
Textbook Question
Simplify each expression. See Example 1. (5x²y) (-3x³y⁴)
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Textbook Question
Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. (-4m²/tp²)⁴
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Textbook Question
CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. The polynomial 2x⁵ - x + 4 is a trinomial of degree _________.
Textbook Question
CONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms (2x/5) • (10/x²)
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Textbook Question
Match each expression in Column I with its equivalent in Column II. See Example 3. I II. a. 6° A. 0 b. -6° B. 1 c. (-6)° C. -1 d. -(-6)° D. 6 E. -6