Textbook Question
Evaluate each expression 27^(-4/3)
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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 69
Simplify using properties of exponents.
Verified step by step guidance1
Identify the expression to simplify: \([5x^{2\/3}][4x^{1\/4}]\).
Use the property of exponents that states when multiplying terms with the same base, you add the exponents: \(x^{a} \cdot x^{b} = x^{a+b}\).
Multiply the coefficients (numbers) separately: \(5 \times 4\).
Add the exponents of \(x\): \(\frac{2}{3} + \frac{1}{4}\).
Write the simplified expression as the product of the multiplied coefficients and the base with the new exponent: \((5 \times 4) x^{(\frac{2}{3} + \frac{1}{4})}\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Properties of Exponents
Properties of exponents are rules that simplify expressions involving powers. Key rules include multiplying powers with the same base by adding their exponents, and raising a power to another power by multiplying exponents. These properties help combine and simplify expressions efficiently.
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Multiplying Expressions with Exponents
When multiplying expressions with the same base, you add the exponents while keeping the base unchanged. For example, x^a * x^b = x^(a+b). This rule is essential for simplifying products of exponential terms.
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Fractional Exponents
Fractional exponents represent roots and powers simultaneously. For instance, x^(m/n) means the nth root of x raised to the mth power. Understanding fractional exponents allows you to manipulate and simplify expressions involving roots and powers.
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Related Practice
Textbook Question
In Exercises 65–92, factor completely, or state that the polynomial is prime. 2x4−162
Textbook Question
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. −2 and 5
Textbook Question
In Exercises 69–82, simplify each complex rational expression. (x/3−1)/(x−3)
Textbook Question
Simplify the radical expressions in Exercises 67–74, if possible. ³√150
Textbook Question
In Exercises 33–68, add or subtract as indicated. (4x2+x−6)/(x2+3x+2)−3x/(x+1)+5/(x+2)
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