Question

How do you do these?

Answer 1

$\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}\\ ----------------------------$$\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}$