Question

If
$\sqrt{2 \sqrt{4 \sqrt{2 \sqrt{4 \sqrt{2 } } } } } = {32}^{a}$
Then find the value of a
please elaborate your answer
please............

Answer 1

$\sqrt{2 \sqrt{4 \sqrt{2 \sqrt{4 \sqrt{2} } } } } = {32}^{a} \\ \sqrt{4 \sqrt{2} \times 2 \sqrt{2} } = {32}^{a} \\ \sqrt{16} = {32}^{a} \\ {2}^{2} = {2}^{5a} \\ 2 = 5a \\ a = \frac{2}{5}$