Question

square root of 5th power of 121. write in the form of rational indices please explain​

Answer 1

$Square \: root \: of \: 5^{th} \: power \: of \: 121$

$= \sqrt{\sqrt[5] { 121}}$

$= \sqrt[2 \times 5 ] { 11^{2}}$

$= \sqrt[10] { 11^{2}}$

$= ( 11^{2})^{\frac{1}{10}}$

$= 11^{2 \times \frac{1}{10}}$

$= 11^{\frac{1}{5}}$

Therefore.,

$\red{Square \: root \: of \: 5^{th} \: power \: of \: 121}$

$\green {= 11^{\frac{1}{5}}}$

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