Domanda del libro di testo
Write each number in decimal notation without the use of exponents.
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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 69
Simplify using properties of exponents.
Guida verificata passo dopo passo1
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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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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Rational Exponents
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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07:07Introduction to Exponents
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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04:06Rational Exponents
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