Question

How is the process of this operation? sqrt%7Bz%2B5%7D%20%7D%20" id="TexFormula1" title=" \frac{ \sqrt[6]{z+5} }{ \sqrt{z+5} } " alt=" \frac{ \sqrt[6]{z+5} }{ \sqrt{z+5} } " align="absmiddle" class="latex-formula">

Answer 1

$a^\frac{n}{m}=\sqrt[m]{a^n}\\---------------\\\\ \dfrac{ \sqrt[6]{z+5} }{ \sqrt{z+5} } =(z+5)^\frac{1}{6}:(z+5)^\frac{1}{2}\\\\/use:a^n\cdot a^m=a^{n+m}/\\\\=(z+5)^{\frac{1}{6}+\frac{1}{2}}=(z+5)^{\frac{1}{6}+\frac{3}{6}}=(z+5)^\frac{4}{6}=(z+5)^\frac{2}{3}\\\\=\sqrt[3]{(z+5)^2}=\sqrt[3]{z^2+2z\cdot5+5^2}=\sqrt[3]{z^2+10z+25}$