Question

Which is equivalent to 3 square root 8^1/4?
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Answer 1

$a^\frac{m}{n}=\sqrt[n]{a^m}\\\\(a^n)^m=a^{nm}\\\\3\sqrt{8^\frac{1}{4}}=3\cdot\sqrt(2^3)^\frac{1}{4}}=3\sqrt{2^{3\cdot\frac{1}{4}}}=3\sqrt{2^\frac{3}{4}}=3\cdot\left(2^\frac{3}{4}\right)^\frac{1}{2}\\\\=3\cdot2^{\frac{3}{4}\cdot\frac{1}{2}}=3\cdot2^\frac{3}{8}\\\\\text{Answer:}\\3\cdot2^\frac{3}{8}=3\sqrt[8]{2^3}=3\sqrt[8]8$