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Combine your skills of working with exponents and manipulating expressions for radical glory.

What is the value of \(\sqrt{2} \times \sqrt{6} \times \sqrt{27}?\)

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Simplify \((\sqrt{x} + \sqrt{3})(\sqrt{x} - \sqrt{3})\)

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\(\sqrt[2]{x} \times \sqrt[4]{x} \times \sqrt[6]{x} \times \sqrt[n]{x} = x\) for all \(x > 0\)

What is the value of \(n?\)

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\(f(x) = (\sqrt{x^{2} + a})(\sqrt{x^{2} - a})\)

For what value(s) of \(a\) will the domain of \(f\) be \(\mathbb{R}?\)

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Simplify \(\sqrt[9]{x^{3}}\)

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