Re-write the expression in rational form.

Question

asked Dec 20, 2022 170k views

1 Answer

Florianbaethge · Answer 1 · 2022-12-27T15:40:53+0000

Given:

$x^{(5)/(4)}=100$

$x=\sqrt[a]{100}^b$

To find:

The values of a and b.

Solution:

We have,

$x^{(5)/(4)}=100$

It can be written as

$x^{(5)/(4)* (4)/(5)}=100^{(4)/(5)}$

$x^(1)=\left[100^{(1)/(5)}\right]^4$
$[\because a^(mn)=(a^m)^n]$

$x=\left[\sqrt[5]{100}\right]^4$
$[\because a^{(1)/(n)}=\sqrt[n]{a}]$

$x=\sqrt[5]{100}^4$

On comparing this with
$x=\sqrt[a]{100}^b$ , we get

a=5

b=4

Therefore, the value of a is 5 and value of b is 4.