Textbook Question
Fill in the blank(s) to correctly complete each sentence.
The graph of ƒ(x) = -√x is a reflection of the graph of y = √x across the ___-axis.
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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.3.19
Simplify each expression. See Example 1. (5x²y) (-3x³y⁴)
Verified step by step guidance1
Identify the expression to simplify: \((5x^{2}y)(-3x^{3}y^{4})\).
Apply the associative property of multiplication to group the coefficients and the variables separately: \((5 \times -3)(x^{2} \times x^{3})(y \times y^{4})\).
Multiply the coefficients: \(5 \times -3 = -15\).
Use the product of powers property for the variables with the same base: \(x^{2} \times x^{3} = x^{2+3} = x^{5}\) and \(y \times y^{4} = y^{1+4} = y^{5}\).
Combine all parts to write the simplified expression: \(-15x^{5}y^{5}\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Multiplication of Monomials
Multiplying monomials involves multiplying their coefficients (numerical parts) and then applying the laws of exponents to variables with the same base. For example, (5x²y) × (-3x³y⁴) requires multiplying 5 and -3, then combining powers of x and y.
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Determining Different Coordinates for the Same Point
Laws of Exponents
When multiplying variables with the same base, add their exponents. For instance, x² × x³ equals x^(2+3) = x⁵. This rule applies to all variables involved in the expression to simplify powers correctly.
Recommended video:
4:35Intro to Law of Cosines
Handling Negative Coefficients
When multiplying coefficients, consider their signs. Multiplying a positive number by a negative number results in a negative product. In the example, 5 × (-3) equals -15, which affects the overall sign of the simplified expression.
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5:35Introduction to Quadratic Equations
Related Practice
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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Textbook Question
Simplify each expression. See Example 1. 9³ • 9⁵
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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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