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Q. Assertion–Reason Type Question
Statement-1: \( \left(\sqrt[m]{\sqrt[n]{a}}\right)^{mn} = a \)
Statement-2: \( ((a^m)^n)^p = a^{mnp} \)
✏️ Solution
\( \sqrt[n]{a} = a^{1/n} \)
\( \sqrt[m]{\sqrt[n]{a}} = (a^{1/n})^{1/m} = a^{1/(mn)} \)
\( \left(a^{1/(mn)}\right)^{mn} = a \)
So Statement-1 is TRUE
Statement-2 is also TRUE (law of exponents)
Statement-2 correctly explains Statement-1
Correct Option: (a)
\( \boxed{\text{(a)}} \)