Question

Express as a power of 2
(2/root8)^3

Answer 1

`\left((2)/(\sqrt 8) \right)^3\\\\\\=\left((2)/(2\sqrt 2) \right)^3\\\\\\=\left(\frac 1{\sqrt 2} \right)^3\\\\\\=\left[\left(\sqrt2 \right)^(-1) \right]^3\\\\\\=\left(\sqrt 2 \right)^(-3)\\\\\\=\left(2^(\tfrac 12) \right)^(-3)\\\\\\=2^(-\tfrac 32)`