Question

Which expression is equivalent to
4^sqrt 6 / 3^sqrt2

Answer 1

C

Step-by-step explanation:

Answer 2

Answer: Choice C

`\frac{\sqrt[12]{55,296}}{2}`

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Step-by-step explanation:

Recall the process to rationalize the denominator is to multiply top and bottom by the denominator expression. This only works if we have a square root in the denominator.

For cube roots, we'll need to multiply two copies of the denominator to top and bottom. This will get us three copies of
`\sqrt[3]{2}` so that the cube root goes away.

Check out the steps below to see what I mean:

`\frac{\sqrt[4]{6}}{\sqrt[3]{2}}\\\\\\\frac{\sqrt[4]{6}\sqrt[3]{2}\sqrt[3]{2}}{\sqrt[3]{2}\sqrt[3]{2}\sqrt[3]{2}}\\\\\\\frac{6^(1/4)*2^(1/3)*2^(1/3)}{\left(\sqrt[3]{2}\right)^3}\\\\\\(6^(3/12)*2^(4/12)*2^(4/12))/(2)\\\\\\(\left(6^3*2^4*2^4\right)^(1/12))/(2)\\\\\\(\left(55,296\right)^(1/12))/(2)\\\\\\\frac{\sqrt[12]{55,296}}{2}\\\\\\`

In short,

`\frac{\sqrt[4]{6}}{\sqrt[3]{2}}=\frac{\sqrt[12]{55,296}}{2}`

We have the 12th root of 55,296 all over top the integer 2. The "2" is not part of the 12th root. This shows why choice C is the final answer.