Textbook Question
Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. (r⁸/s²)³
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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.3.11
Simplify each expression. See Example 1. (-4x⁵) (4x²)
Verified step by step guidance1
Identify the properties of exponents and multiplication that apply. When multiplying terms with the same base, you multiply the coefficients and add the exponents of the variables.
Multiply the coefficients: here, multiply -4 and 4, which gives \(-4 \times 4\).
Apply the product rule for exponents to the variable part: since the bases are the same (both are \(x\)), add the exponents \(5\) and \(2\) using \(x^{5} \times x^{2} = x^{5+2}\).
Combine the results from the coefficient multiplication and the exponent addition to write the simplified expression as a product of the new coefficient and the variable with the summed exponent.
Write the final simplified expression in the form \(ax^{b}\), where \(a\) is the product of the coefficients and \(b\) is the sum of the exponents.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Product of Powers Property
When multiplying expressions with the same base, add the exponents. For example, x^a * x^b = x^(a+b). This property simplifies expressions involving powers of variables.
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05:40
Introduction to Dot Product
Multiplication of Coefficients
Multiply the numerical coefficients separately from the variables. For instance, in (-4x⁵)(4x²), multiply -4 and 4 to get -16 before combining the variable parts.
Recommended video:
5:35Introduction to Quadratic Equations
Simplifying Algebraic Expressions
Combine like terms and apply arithmetic operations to rewrite expressions in simpler forms. This involves using exponent rules and basic multiplication to reduce complexity.
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6:36Simplifying Trig Expressions
Related Practice
Textbook Question
Simplify each expression. See Example 1. n⁶ • n⁴ • n
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Textbook Question
CONCEPT PREVIEW Work each problem. Match each polynomial in Column I with its factored form in Column II. I II a. x² + 10xy + 25y² A. (x + 5y) (x - 5y) b. x² - 10xy + 25y² B. (x + 5y)² c. x² - 25y² C. (x - 5y)² d. 25y² - x² D. (5y + x) (5y - x)
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Textbook Question
Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. - ( x³y⁵/z)⁰
Textbook Question
Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. (-6x²)³
Textbook Question
Simplify each expression. See Example 1. (-3m⁴) (6m²) (-4m⁵)