Question 2: \((iv)\) \(\quad\) \( \large{\sqrt[7]{\frac{x^{14} \times y^{21} \times z^{35}}{y^{14} \times z^{7}}}}\)
Solution:
\[\begin{align*}
&=\sqrt[7]{\frac{x^{14} \times y^{21} \times z^{35}}{y^{14} \times z^{7}}} \\
&=\left(\frac{x^{14} \times y^{21} \times z^{35}}{y^{14} \times z^{7}}\right)^{\frac{1}{7}}\\
&={\frac{x^{14\times\frac{1}{7}} \times y^{21\times\frac{1}{7}} \times z^{35\times\frac{1}{7}}}{y^{14\times\frac{1}{7}} \times z^{7\times\frac{1}{7}}}} \\
&=\frac{x^{2} \times y^{3} \times z^{5}}{y^{2} \times z}\\
&=x^{2} \times y^{3-2} \times z^{5-1}\\
&=x^{2} y z^{4}\\
\end{align*}\]