Use positive exponents to rewrite the following expression. Assume that variables represent positive numbers.
\[
\sqrt{x \cdot \sqrt[6]{x}}
\]
$\sqrt{x \cdot \sqrt[6]{x}}=$
(Use integers or fractions for any numbers in the expression.)

Answer

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Answer

Final Answer: $\boxed{x^{7/12}}$

Steps

Step 1 ：Rewrite the expression using exponents: $\sqrt{x \cdot \sqrt[6]{x}} = (x \cdot x^{1/6})^{1/2}$

Step 2 ：Simplify the expression by applying the rules of exponents: $(x \cdot x^{1/6})^{1/2} = x^{1/2} \cdot x^{1/12}$

Step 3 ：Combine terms with the same base by adding the exponents: $x^{1/2} \cdot x^{1/12} = x^{1/2 + 1/12} = x^{7/12}$

Step 4 ：Final Answer: $\boxed{x^{7/12}}$