Textbook Question
Evaluate each exponential expression: 5-3• 5
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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 24
Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0.
Verified step by step guidance1
Identify the expression to simplify: \(\sqrt{\frac{1}{49}}\).
Recall that the square root of a quotient can be written as the quotient of the square roots: \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\).
Apply this property to rewrite the expression as \(\frac{\sqrt{1}}{\sqrt{49}}\).
Simplify the square roots individually: \(\sqrt{1} = 1\) and \(\sqrt{49} = 7\).
Write the simplified expression as \(\frac{1}{7}\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Quotient Rule for Radicals
The quotient rule for radicals states that the square root of a quotient is equal to the quotient of the square roots, i.e., √(a/b) = √a / √b, provided b ≠ 0. This rule allows simplification of expressions involving square roots of fractions.
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Product, Quotient, and Power Rules of Logs
Simplifying Square Roots
Simplifying square roots involves finding the prime factorization of the number under the root and extracting perfect squares. For example, √49 = 7 because 49 is a perfect square. Simplification makes expressions easier to interpret and use.
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02:20Imaginary Roots with the Square Root Property
Properties of Square Roots with Positive Variables
When variables are positive (x > 0), the square root of x² simplifies directly to x, avoiding absolute value considerations. This assumption simplifies radical expressions and ensures the principal (non-negative) root is taken.
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02:20Imaginary Roots with the Square Root Property
Related Practice
Textbook Question
Multiply or divide as indicated.
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Textbook Question
Simplify each exponential expression in Exercises 23–64.
Textbook Question
Evaluate each exponential expression: (-3)3 (-2)2
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Textbook Question
Evaluate each exponential expression: 2^(-4) + 4^(-1)
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Textbook Question
In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. 2x^2+5x−3