Question

Which expression is equivalent to sqrt2/^3sqrt2

Answer 1

The given expression is $\frac{\sqrt{2}}{\sqrt[3]{2}}$

This can be simplified using the radical properties as below

$\\\ \frac{\sqrt{2}}{\sqrt[3]{2}}=\frac{2^{\frac{1}{2}}}{2^\frac{1}{3}} \\\\ \frac{\sqrt{2}}{\sqrt[3]{2}}=\frac{2^{\frac{1}{2}}}{2^\frac{1}{3}}$

Now using exponent properties we can write

$\\\ \frac{\sqrt{2}}{\sqrt[3]{2}}=\frac{2^{\frac{1}{2}}}{2^\frac{1}{3}}=2^{\frac{1}{2}-\frac{1}{3}} \\\\\frac{\sqrt{2}}{\sqrt[3]{2}}=2^{\frac{3-2}{6}}=2^\frac{1}{6}\\\\= \sqrt[6]{2}$

Answer 2

Answer: Option B

^6 sqrt 2

Step-by-step explanation: