Question

Write the following number in the form of a rational indices.

Square root of 5th power of 121

Answer 1

It is known that,

${\displaystyle a^{\frac{m}{n}}={\left(am\right)}^{\frac{1}{n}}}$ means 'nth root of mth power of a'.

${\displaystyle a^{\frac{m}{n}}={\left(a{m}^{\frac{1}{n}}\right)}^m}$ means 'm^th power of nth root of a'.

Square root of 5^th power of 121

= ${\displaystyle {\left\{{\left(121\right)}^5\right\}}^{\frac{1}{2}}}$

= ${\displaystyle {\left(121\right)}^{\frac{5}{2}}}$