Question

Re-write the expression in rational form.

Answer 1

Given:

$x^{\frac{5}{4}}=100$

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

To find:

The values of a and b.

Solution:

We have,

$x^{\frac{5}{4}}=100$

It can be written as

$x^{\frac{5}{4}\times \frac{4}{5}}=100^{\frac{4}{5}}$

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

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

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

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.