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 95

Textbook Question

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (y^7/3)(y^-4/3)

Verified step by step guidance

Identify the expression to simplify: \((y^{7/3})(y^{-4/3})\).

Apply the property of exponents: \(a^m \cdot a^n = a^{m+n}\).

Combine the exponents: \(y^{7/3 + (-4/3)}\).

Simplify the exponent by adding: \(y^{(7/3) + (-4/3)} = y^{(7/3 - 4/3)}\).

Calculate the exponent: \(y^{3/3}\), which simplifies to \(y^1\).

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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 (a^m * a^n = a^(m+n)) and the power of a power (a^m)^n = a^(m*n). Understanding these properties is essential for simplifying expressions involving exponents, especially when combining terms with the same base.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent (a^-n = 1/a^n). This concept is crucial when simplifying expressions, as it allows for the conversion of negative exponents into a more manageable form, ensuring that the final answer adheres to the requirement of not having negative exponents.

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves combining like terms and applying exponent rules to reduce the expression to its simplest form. This process often includes eliminating negative exponents and ensuring that all variables are expressed positively, which is a common requirement in algebraic problems.