Observe 4^1/6 = (2^2)^1/6 = 2^2× (1/6) = 2^1/3 Hence 2^1/24^1/6 = 2^1/22^1/3 = 2^(1/2) (1/3) = 2^1/6 . ...

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Exponents with Like Bases

Simplify: 2...

Question

Simplify: $\frac{2^{1 / 2}}{4^{1 / 6}}$

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Solution

Observe
$4^{1 / 6} = (2^{2})^{1 / 6} = 2^{2 \times (1 / 6)} = 2^{1 / 3}$
Hence
$\frac{2^{1 / 2}}{4^{1 / 6}} = \frac{2^{1 / 2}}{2^{1 / 3}} = 2^{(1 / 2) - (1 / 3)} = 2^{1 / 6}$ .

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