Given:
[tex]x^{\frac{5}{4}}=100[/tex]
[tex]x=\sqrt[a]{100}^b[/tex]
To find:
The values of a and b.
Solution:
We have,
[tex]x^{\frac{5}{4}}=100[/tex]
It can be written as
[tex]x^{\frac{5}{4}\times \frac{4}{5}}=100^{\frac{4}{5}}[/tex]
[tex]x^{1}=\left[100^{\frac{1}{5}}\right]^4[/tex] [tex][\because a^{mn}=(a^m)^n][/tex]
[tex]x=\left[\sqrt[5]{100}\right]^4[/tex] [tex][\because a^{\frac{1}{n}}=\sqrt[n]{a}][/tex]
[tex]x=\sqrt[5]{100}^4[/tex]
On comparing this with [tex]x=\sqrt[a]{100}^b[/tex], we get
[tex]a=5[/tex]
[tex]b=4[/tex]
Therefore, the value of a is 5 and value of b is 4.
