[tex]\bf 6\sqrt[4]{405}\quad now\to
\begin{cases}
405\to 3\cdot 3\cdot 3\cdot 3\cdot 5\\
\qquad 3^4\cdot 5
\end{cases}
\\ \quad \\
6\sqrt[4]{3^4\cdot 5}\implies 6\cdot 3\sqrt[4]{5}\\
----------------------------\\
[/tex][tex]\bf 3\sqrt{49x^9y^{16}}\quad now\to
\begin{cases}
49\to 7\cdot 7\to 7^2\\
x^9\to x^{2+2+2+2+1}\\
\qquad x^2\cdot x^2\cdot x^2\cdot x^2\cdot x^1\\
\qquad (x^2)^4\cdot x\\
y^{16}\to y^{2+2+2+2+2+2+2+2}\\
\qquad y^2\cdot y^2\cdot y^2\cdot y^2\\
\qquad \cdot y^2\cdot y^2\cdot y^2\cdot y^2\\
\qquad (y^2)^8
\end{cases}
\\ \quad \\
3\sqrt{7^2(x^2)^4x(y^2)^8}\implies 3\sqrt{7^2(x^4)^2x(y^8)^2}
\\ \quad \\
3\cdot 7\cdot x^4\cdot y^8\sqrt{x}\implies 21x^4y^8\sqrt{x}[/tex]
