Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
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]
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. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.