Question

Write the following expression in radical form: x^3/2​

Answer 1

Answer:

$x\sqrt{x}$

Step-by-step explanation:

Given:

The given expression is.

$x^{\frac{3}{2}}$

Now, we need to write the given expression in radical form.

Solution:

First, we can rewrite the term as:

$x^{3\times \frac{1}{2}$

Now, we can use this rule of exponents to rewrite the term again:

$x^{a\times b} = (x^{a})^{b}$

$x^{3\times \frac{1}{2}} = (x^{3})^{\frac{1}{2}}$

Now, we can use this rule to write the term as an radical:

$x^{\frac{1}{n}} = \sqrt[n]{x}$

$(x^{3})^{\frac{1}{2}} = \sqrt[2]{x^{3}}$

$(x^{3})^{\frac{1}{2}} = x\sqrt{x}$

Therefore, the redical form of the given expression is $x\sqrt{x}$