how can $\sqrt{2}/4=1/2^{3/2}$

Question

$\sqrt{2}/4=1/2^{3/2}$ this is a subpart of a work example question I have but I don't understand how I can convert the first part into the second.

Answer 1

$$\frac{\sqrt2}{2^2} = \frac{2^\frac{1}{2}}{2^2} =2^{-\frac{3}{2}} = \frac{1}{2^\frac{3}{2}}$$

Answer 2

$$\require{cancel}\frac{\sqrt{2}}{4}=\frac{\cancel{\sqrt{2}}}{\cancel{\sqrt{2}}\sqrt{2}\sqrt{2}\sqrt{2}}=\frac{1}{\sqrt{2}^3}=\frac{1}{(2^{1/2})^3}=\frac{1}{2^{3/2}}.$$

Or,

$$\frac{\sqrt{2}}{4}=\frac{2^{1/2}}{2^2} = 2^{(1/2)-2} = 2^{-3/2}=\frac{1}{2^{3/2}}.$$

Answer 3

Rationalize the numerator $$\frac{\sqrt{2}}{4}=\frac{\sqrt{2}×\sqrt{2}}{4×\sqrt{2}}$$ $$=\frac{2}{4\sqrt{2}}=\frac{1}{2\sqrt{2}}=\frac{1}{\sqrt{2^2×2}}=\frac{1}{\sqrt{2^3}}=\frac{1}{(2^3)^\frac{1}{2}}=\frac{1}{2^\frac{3}{2}}$$