Question

Simplify completely. $$ \sqrt[3]{x^{9} y^{16}} $$

   Simplify completely.
$$
\sqrt[3]{x^{9} y^{16}}
$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Sherri Messersmith 3rd Edition

Chapter 10, Problem 44

Instant Answer

Solved by Expert Narayan Hari

02/19/2021

Step 1

We can rewrite this as $(x^{9} y^{16})^{1/3}$. Show more…

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Simplify completely. $$ \sqrt[3]{x^{9} y^{16}} $$

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Key Concepts

Radical Expressions

This concept involves understanding that radicals, such as cube roots, represent the inverse operation of exponentiation. For example, the cube root of an expression is equivalent to raising that expression to the power of 1/3. This relationship is essential in converting between radical notation and rational exponents, which simplifies the manipulation of expressions.

Properties of Exponents

This concept covers the rules governing exponent operations, including the product of powers rule, power of a power rule, and the rules for multiplying and dividing expressions with exponents. These rules are particularly important when simplifying radical expressions containing variables raised to powers, as one can express radicals as fractional exponents and then apply exponent rules for simplification.

Simplification of Radicals

This involves identifying and extracting perfect power factors from under the radical sign. When an exponent in the radicand is a multiple of the radical’s index, that factor can be taken out of the radical. Recognizing these factors is key to rewriting the expression in its simplest form, combining the properties of exponents and radical notation.

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