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In Exercises 15–58, find each product. (7x3+5)(x2−2)
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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 29
Simplify each exponential expression:
Guida verificata passo dopo passo1
Identify the expression to simplify: \((-5x^{3}y^{2})(-2x^{-11}y^{-2})\).
Multiply the coefficients (numbers) together: \(-5 \times -2\).
Apply the product rule for exponents to the \(x\) terms: \(x^{3} \times x^{-11} = x^{3 + (-11)}\).
Apply the product rule for exponents to the \(y\) terms: \(y^{2} \times y^{-2} = y^{2 + (-2)}\).
Combine the results from the coefficient multiplication and the simplified variables to write the final simplified expression.
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Laws of Exponents
The laws of exponents govern how to simplify expressions involving powers. Key rules include multiplying powers with the same base by adding their exponents, and handling negative exponents by rewriting them as reciprocals. These rules allow simplification of expressions like x^a * x^b = x^(a+b).
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Rational Exponents
Multiplication of Algebraic Expressions
When multiplying algebraic expressions, multiply the coefficients (numerical parts) separately from the variables. For variables with exponents, apply the laws of exponents. This process helps combine terms systematically to simplify the overall expression.
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05:09Introduction to Algebraic Expressions
Handling Negative Exponents
Negative exponents indicate the reciprocal of the base raised to the positive exponent, e.g., x^(-n) = 1/x^n. Understanding this allows rewriting terms with negative exponents into fractions or adjusting exponents during multiplication to simplify expressions correctly.
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6:37Zero and Negative Rules
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In Exercises 15–58, find each product. (7x2−2)(3x2−5)
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