Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Radical Expressions

College Algebra

0. Review of Algebra

Radical Expressions

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1:36 minutes

Problem 91

Textbook Question

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (3^1/2)(3^3/2)

Verified step by step guidance

insert step 1> Identify the expression to simplify: \((3^{1/2})(3^{3/2})\).

insert step 2> Use the property of exponents that states \(a^m \cdot a^n = a^{m+n}\).

insert step 3> Add the exponents: \(\frac{1}{2} + \frac{3}{2}\).

insert step 4> Simplify the sum of the exponents: \(\frac{1}{2} + \frac{3}{2} = \frac{4}{2}\).

insert step 5> Rewrite the expression with the simplified exponent: \(3^{2}\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Exponents and Their Properties

Exponents represent repeated multiplication of a base number. Key properties include the product of powers, which states that when multiplying like bases, you add the exponents. For example, a^m * a^n = a^(m+n). Understanding these properties is essential for simplifying expressions involving exponents.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent. For instance, a^(-n) = 1/(a^n). In this problem, the instruction to write answers without negative exponents means we must express all terms in a positive exponent format, ensuring clarity and adherence to mathematical conventions.

Radicals and Rational Exponents

Radicals can be expressed as rational exponents, where the nth root of a number is represented as a fractional exponent. For example, the square root of a is written as a^(1/2). This concept is crucial for simplifying expressions that involve roots, as it allows for the application of exponent rules to combine and simplify terms effectively.