Domanda del libro di testo
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, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- 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
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema R.3.19
Simplify each expression. See Example 1. (5x²y) (-3x³y⁴)
Guida verificata passo dopo passo1
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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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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6:02
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.
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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
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