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In Exercises 49–56, factor each perfect square trinomial. x^2−14x+49
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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 51
Simplify each exponential expression in Exercises 23–64.
Guida verificata passo dopo passo1
Identify the given expression: \(\frac{25a^{13}b^{4}}{-5a^{2}b^{3}}\).
Separate the coefficients and the variables to simplify each part individually: \(\frac{25}{-5} \times \frac{a^{13}}{a^{2}} \times \frac{b^{4}}{b^{3}}\).
Simplify the coefficients: \(\frac{25}{-5} = -5\).
Apply the quotient rule for exponents to the variables: \(\frac{a^{13}}{a^{2}} = a^{13-2} = a^{11}\) and \(\frac{b^{4}}{b^{3}} = b^{4-3} = b^{1}\).
Combine the simplified parts to write the final simplified expression: \(-5a^{11}b\).
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Laws of Exponents
The laws of exponents govern how to simplify expressions involving powers. Key rules include dividing powers with the same base by subtracting exponents, multiplying powers by adding exponents, and handling negative exponents by taking reciprocals. These rules allow simplification of expressions like a^13 / a^2 = a^(13-2) = a^11.
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Rational Exponents
Simplifying Algebraic Fractions
Simplifying algebraic fractions involves reducing the numerator and denominator by canceling common factors. This includes factoring expressions and applying exponent rules to variables. The goal is to write the expression in its simplest form, making it easier to interpret or use in further calculations.
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05:07Simplifying Algebraic Expressions
Handling Negative Signs in Fractions
When simplifying fractions, the negative sign can be placed in front of the entire fraction, in the numerator, or in the denominator. Understanding how to correctly manage the negative sign ensures the simplified expression accurately reflects the original value, such as writing -5a^2 b^3 in the denominator as a negative fraction.
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05:45Radical Expressions with Fractions
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