√169a⁶x¹³

To simplify the expression \(\sqrt{169a^6x^{13}}\), we can break it down as follows:

1. Square root of 169: \(\sqrt{169} = 13\)

2. Square root of \(a^6\): \(\sqrt{a^6} = a^{6/2} = a^3\)

3. Square root of \(x^{13}\): We can rewrite \(x^{13}\) as \(x^{12} \cdot x^1\). Thus, \(\sqrt{x^{13}} = \sqrt{x^{12} \cdot x^1} = \sqrt{x^{12}} \cdot \sqrt{x^1}\) \(\sqrt{x^{12}} = x^{12/2} = x^6\), and \(\sqrt{x^1} = \sqrt{x} = x^{1/2}\). Therefore, \(\sqrt{x^{13}} = x^6 \sqrt{x}\).

Putting it all together, we have:

\[ \sqrt{169a^6x^{13}} = 13a^3x^6\sqrt{x} \]

So, the simplified form is:

\[ 13a^3x^6\sqrt{x} \]