Question

I need help so much please help the attachment below is the question i need help on

Answer 1

`\frac{\sqrt[12]{55296}}{2}`

Explanation:

Rationalize the denominator, then use a common root for the numerator.

`\frac{\sqrt[4]{6}}{\sqrt[3]{2}}=\frac{(2\cdot 3)^{(1)/(4)}}{2^{(1)/(3)}}\\\\=\frac{(2\cdot 3)^{(1)/(4)}}{2^{(1)/(3)}}\cdot\frac{2^{(2)/(3)}}{2^{(2)/(3)}}=\frac{2^{(1)/(4)+(2)/(3)}3^{(1)/(4)}}{2}\\\\=\frac{2^{(11)/(12)}3^{(3)/(12)}}{2}=\frac{\sqrt[12]{2^(11)3^(3)}}{2}\\\\=\frac{\sqrt[12]{55296}}{2}`