Question

Select the correct answer. Rewrite the following expression.

Answer 1

The algebraic expression $x^{10/3}$ is equivalent to the algebraic expression $x^{3}\cdot \sqrt[3]{x}$. 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:

$x^{m/n} = \sqrt[n]{x^{m}} = \left(\sqrt[n]{x}\right)^{m}$   (1)

$x^{m+n} = x^{m}\cdot x^{n}$   (2)

$x^{m\cdot n} = \left(x^{m}\right)^{n} = \left(x^{n}\right)^{m}$   (3)

Where:

• m, n - Exponents
• x - Base

And also by apply the definition of power.

If we know that the given expression is $x^{10/3}$, then the equivalent expression is:

$x^{10/3} = \sqrt[3]{x^{10}} = \sqrt[3]{x^{9}\cdot x} = \sqrt[3]{x^{9}}\cdot \sqrt[3]{x} = x^{3}\cdot \sqrt[3]{x}$

The algebraic expression $x^{10/3}$ is equivalent to the algebraic expression $x^{3}\cdot \sqrt[3]{x}$. Thus, the right choice is option D.

To learn more on roots, we kindly invite to check this verified question: brainly.com/question/1527773