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Simplify the expression [ cuberoot( cuberoot( a⁹)) ]⁴ * [ cuberoot( cuberoot( a⁹)) ]⁴.
- a¹⁶
- a¹²
- a⁸
- a⁴
Correct answer: a⁸
Solution
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.
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