Simplify completely. √(y^9)

Name: Problem 39, Chapter 10: Beginning and Intermediate Algebra
Uploaded: 2021-02-19T18:39:14-08:00
Duration: 1 min 1 s
Channel: Narayan Hari
Description: Simplify completely. √(y^9)

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Key Concepts

Properties of Exponents

The properties of exponents, including rules like a^(m+n) = a^m * a^n and (a^m)^n = a^(m*n), are fundamental in algebra for simplifying expressions with powers. These rules allow one to reorganize and simplify expressions by decomposing exponents into sums or products, thereby making it possible to extract perfect powers from under radical signs.

Rational Exponents

Rational exponents express roots as fractional powers; for example, a^(1/n) is equivalent to the nth root of a. This form is particularly useful because it enables one to use the laws of exponents—such as multiplying or adding exponents—to simplify expressions by separating integer parts from fractional parts.

Radical Expressions

Radical expressions involve roots, such as square roots, cube roots, and more generally, nth roots. They can often be rewritten using fractional (or rational) exponents, which allows for the application of exponent rules to simplify the expression further.

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