What is \sqrt[n]{x^{n+2}}*\sqrt[n]{x^{n-2}} ?

The solution to \sqrt[n]{x^{n+2}}*\sqrt[n]{x^{n-2}} is x^2

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simplify \sqrt[n]{x^{n+2}}*\sqrt[n]{x^{n-2}}

simplify

x^{2}

Solution steps

Apply radical rule:

assuming

a \geq 0, b \geq 0

= (x^{n + 2} x^{n - 2})^{\frac{1}{n}}

Simplify

x^{n + 2} x^{n - 2} : x^{2 n}

= (x^{2 n})^{\frac{1}{n}}

Apply radical rule:

assuming

a \geq 0

= x^{\frac{2 n}{n}}

\frac{2 n}{n} = 2

= x^{2}

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What is \sqrt[n]{x^{n+2}}*\sqrt[n]{x^{n-2}} ?
The solution to \sqrt[n]{x^{n+2}}*\sqrt[n]{x^{n-2}} is x^2