The exponential form of `sqrt(sqrt(2)xxsqrt(3))` is

Options

A. `6`
B. `6^((1)/(2))`
C. `6^(-(1)/(2))`
D. `6^((1)/(4))`

Answer

To find the exponential form of \( \sqrt{\sqrt{2} \times \sqrt{3}} \), we can follow these steps:

### Step 1: Simplify the expression inside the square root
We start with the expression:
\[ \sqrt{\sqrt{2} \times \sqrt{3}} \]
Using the property of square roots that states \( \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \), we can combine the square roots:
\[ \sqrt{\sqrt{2} \times \sqrt{3}} = \sqrt{\sqrt{2 \times 3}} = \sqrt{\sqrt{6}} \]

### Step 2: Rewrite the square root in exponential form
The square root can be expressed as an exponent of \( \frac{1}{2} \):
\[ \sqrt{\sqrt{6}} = \sqrt{6^{1}} = 6^{1/2} \]
Now, we can rewrite the square root of 6:
\[ \sqrt{6} = 6^{1/2} \]

### Step 3: Apply the square root again
Now we need to apply the square root again:
\[ \sqrt{6^{1/2}} = (6^{1/2})^{1/2} \]
Using the property of exponents \( (a^m)^n = a^{m \cdot n} \):
\[ (6^{1/2})^{1/2} = 6^{(1/2) \cdot (1/2)} = 6^{1/4} \]

### Final Answer
Thus, the exponential form of \( \sqrt{\sqrt{2} \times \sqrt{3}} \) is:
\[ 6^{1/4} \]