Radical form of (x^2/3 • X ^5/3)^1/2

Question

asked Jul 23, 2024 14.6k views

1 Answer

Cbroughton · Answer 1 · 2024-07-28T12:27:17+0000

The radical form of the expression
$(\frac{x^{(2)/(3) }. x^{(5)/(3) }}{2} )^{(1)/(2) }$ is
$\frac{x^{(7)/(6) }}{√(2) }$ .

To find the radical form of
$(\frac{x^{(2)/(3) }. x^{(5)/(3) }}{2} )^{(1)/(2) }$ , let's simplify it step by step.

First, let's combine the exponents inside the parentheses:

$x^{(2)/(3) }. x^{(5)/(3) }= x^{(2)/(3) +(5)/(3) }= x^{(7)/(3) }$

So, the expression becomes:

$(\frac{x^{(7)/(3) }}{2} )^{(1)/(2) }$

To simplify further, recall that raising something to the power of 1/2 is the same as taking the square root:

$\sqrt{\frac{x^{(7)/(3) }}{2}}$

In radical form:

$\sqrt{\frac{x^{(7)/(3) }}{2}}=\sqrt{\frac{x^{(7)/(3) }}{√(2) } } =\frac{x^{(7)/(3) }}{√(2) }$

Therefore, the radical form of the expression
$(\frac{x^{(2)/(3) }. x^{(5)/(3) }}{2} )^{(1)/(2) }$ is
$\frac{x^{(7)/(6) }}{√(2) }$