Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Select the correct answer.

What is the correct radical form of this expression? [tex]\(\left(32 a^{10} b^{\frac{5}{2}}\right)^{\frac{2}{5}}\)[/tex]

A. [tex]\(\sqrt[5]{\left(32 a^{10} b^{\frac{5}{2}}\right)^2}\)[/tex]

B. [tex]\(\sqrt{\left(32 a^{10} b^{\frac{5}{2}}\right)^5}\)[/tex]

C. [tex]\(\sqrt{\left(32 a^{10} b^{\frac{5}{2}}\right)^{\frac{2}{5}}}\)[/tex]

D. [tex]\(\sqrt{\left(32 a^{10} b^{\frac{5}{2}}\right)^{\frac{1}{5}}}\)[/tex]

Sagot :

GinnyAnswer
Let's analyze the given expression and convert it to its radical form:

We are given the expression: [tex]\(\left(32 a^{10} b^{\frac{5}{2}}\right)^{\frac{2}{5}}\)[/tex].

To convert an expression of the form [tex]\(x^{\frac{m}{n}}\)[/tex] to its radical form, we recognize that it is equivalent to the [tex]\(n\)[/tex]-th root of [tex]\(x\)[/tex] raised to the power of [tex]\(m\)[/tex], or [tex]\(\sqrt[n]{x^m}\)[/tex].

Here, [tex]\(x = 32 a^{10} b^{\frac{5}{2}}\)[/tex], [tex]\(m = 2\)[/tex], and [tex]\(n = 5\)[/tex].

Therefore, the expression [tex]\(\left(32 a^{10} b^{\frac{5}{2}}\right)^{\frac{2}{5}}\)[/tex] can be rewritten in radical form as:

[tex]\[ \sqrt[5]{\left(32 a^{10} b^{\frac{5}{2}}\right)^2} \][/tex]

Thus, the correct answer is:

A. [tex]\(\sqrt[5]{\left(32 a^{10} b^{\frac{5}{2}}\right)^2}\)[/tex]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.