Question

Express the following numbers in index form.
(1) Fifth root of $13$
(2) Sixth root of $9$
(3) Square root of $256$
(4) Cube root of $17$
(5) Eighth root of $100$
(6) Seventh root of $30$

Answer 1

It is known that,
$n^{\text{th}}$ root of $a$ is expressed as $a^{\frac{1}{n}}$.
(1) Fifth root of $13=(13{)}^{\frac{1}{5}}$
(2) Sixth root of $9=9^{\left(\frac{1}{6}\right)}$
(3) Square root of $256=(256{)}^{\frac{1}{2}}$
(4) Cube root of $17=(17{)}^{\frac{1}{3}}$
(5) Eighth root of $100=(100{)}^{\frac{1}{8}}$
(6) Seventh root of $30=(30{)}^{\frac{1}{7}}$