Textbook Question
Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √48x3/√3x
Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- 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
Chapter 1, Problem 27
Evaluate each exponential expression: (33)/(36)
Verified step by step guidance1
Recall the property of exponents that states when dividing powers with the same base, you subtract the exponents: \(\frac{a^m}{a^n} = a^{m-n}\).
Identify the base and the exponents in the expression \(\frac{3^3}{3^6}\). Here, the base is 3, the numerator exponent is 3, and the denominator exponent is 6.
Apply the exponent subtraction rule: \(\frac{3^3}{3^6} = 3^{3-6}\).
Simplify the exponent by performing the subtraction: \(3^{3-6} = 3^{-3}\).
Recognize that a negative exponent means the reciprocal: \(3^{-3} = \frac{1}{3^3}\). This is the simplified form of the expression.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Properties of Exponents
Exponents follow specific rules that simplify expressions, such as when dividing powers with the same base, you subtract the exponents. For example, (a^m)/(a^n) = a^(m-n). This property helps in reducing complex exponential expressions efficiently.
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Base Consistency in Exponents
When working with exponential expressions, the base must be the same to apply exponent rules like multiplication or division. In the given problem, both numerator and denominator have base 3, allowing the use of exponent subtraction.
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Evaluating Powers
After simplifying the exponent expression, you may need to calculate the numerical value by raising the base to the resulting exponent. For example, 3^(3-6) = 3^(-3), which equals 1/(3^3) = 1/27.
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Related Practice
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