To simplify the expression \(\sqrt{x^{13}}\), we can use the property of square roots that states \(\sqrt{a^b} = a^{b/2}\).
Using this property, we have:
\[ \sqrt{x^{13}} = x^{13/2} \]
Next, we can express \(x^{13/2}\) in terms of radicals. The exponent \(13/2\) can be split into an integer part and a fractional part:
\[ \frac{13}{2} = 6 + \frac{1}{2} \]
Thus, we can express this as:
\[ x^{13/2} = x^6 \cdot x^{1/2} = x^6 \cdot \sqrt{x} \]
Combining this, we can write the entire simplification as:
\[ \sqrt{x^{13}} = x^6 \sqrt{x} \]
So the final answer is:
\[ x^6 \sqrt{x} \]
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