JEE Advanced Maths: Basic Maths / Indices questions with solutions

Q1. Simplify the expression [ cuberoot( cuberoot( a⁹)) ]⁴ * [ cuberoot( cuberoot( a⁹)) ]⁴.

1. a¹⁶
2. a¹²
3. a⁸
4. a⁴

Answer: a⁸

Inner: cuberoot(a⁹) = a^(9/3) = a³. Then cuberoot(a³) = a^(3/3) = a¹. So each bracket = (a)⁴ = a⁴. Product of the two brackets = a⁴ * a⁴ = a⁸.