Question

Simplify. Assume that $x \geq 0$ $\sqrt[12]{x^{44}}$

   Simplify. Assume that $x \geq 0$
$\sqrt[12]{x^{44}}$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Margaret L. Lial,… 7th Edition

Chapter 10, Problem 108

Instant Answer

Solved by Expert Nick Johnson

02/11/2022

Step 1

The 12th root of $x^{44}$ can be written as $x^{44/12}$. Show more…

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Simplify. Assume that $x \geq 0$ $\sqrt[12]{x^{44}}$

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Key Concepts

Rational Exponents

This concept involves expressing roots in terms of fractional exponents, which allows easier manipulation of expressions. For example, the 12th root of any expression can be written with an exponent of 1/12.

Exponent Simplification

This refers to applying the laws of exponents, such as reducing a fraction in the exponent by canceling common factors. In this case, an exponent like 44/12 can be reduced to simplest form, making the expression more manageable.

Properties of Radicals and Domain Restrictions

Understanding the properties of radicals involves knowing how to convert between radical notation and exponent form, especially when dealing with even roots. The assumption that the variable is nonnegative ensures that the simplified expression is valid and avoids issues related to absolute values.

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