The algebraic expression [tex]x^{10/3}[/tex] is equivalent to the algebraic expression [tex]x^{3}\cdot \sqrt[3]{x}[/tex]. Thus, the right choice is option D.
How to apply power and root properties to rewrite a given expression
In this question we must apply the following set of algebraic properties to simplify a given expression:
[tex]x^{m/n} = \sqrt[n]{x^{m}} = \left(\sqrt[n]{x}\right)^{m}[/tex] (1)
[tex]x^{m+n} = x^{m}\cdot x^{n}[/tex] (2)
[tex]x^{m\cdot n} = \left(x^{m}\right)^{n} = \left(x^{n}\right)^{m}[/tex] (3)
Where:
And also by apply the definition of power.
If we know that the given expression is [tex]x^{10/3}[/tex], then the equivalent expression is:
[tex]x^{10/3} = \sqrt[3]{x^{10}} = \sqrt[3]{x^{9}\cdot x} = \sqrt[3]{x^{9}}\cdot \sqrt[3]{x} = x^{3}\cdot \sqrt[3]{x}[/tex]
The algebraic expression [tex]x^{10/3}[/tex] is equivalent to the algebraic expression [tex]x^{3}\cdot \sqrt[3]{x}[/tex]. Thus, the right choice is option D.
To learn more on roots, we kindly invite to check this verified question: https://brainly.com/question/1527773
