Answer:
[tex](\sqrt[4]{9})(\sqrt{9})\div \sqrt[4]{9^5}=\frac{\textbf{1}}{\sqrt{\textbf{9}}}[/tex]
Step-by-step explanation:
Given expression is
[tex](\sqrt[4]{9})(\sqrt{9})\div \sqrt[4]{9^5}[/tex]
The above expression can be written as
[tex]\frac{(9)^{\tfrac{1}{4}}(9^{\tfrac{1}{2}})}{(9^5)^{\tfrac{1}{4}}}[/tex]
[tex]=\frac{9^{\tfrac{1+2}{4}}}{9^{\tfrac{5}{4}}}[/tex] (by using the formula [tex]a^m\times a^n=a^{m+n}[/tex])
[tex]=9^{\tfrac{3}{4}}\times 9^{\tfrac{-5}{4}}[/tex] (by using the formulae [tex]{(a^m)}^n=a^{mn}[/tex] and [tex]\frac{a^m}{a^n}=a^{m-n}[/tex])
[tex]=9^{\tfrac{-2}{4}}[/tex]
[tex]=9^{\tfrac{-1}{2}}[/tex]
[tex]=\frac{1}{9^{\tfrac{1}{2}}}[/tex]
[tex](\sqrt[4]{9})(\sqrt{9})\div \sqrt[4]{9^5}=\frac{\textbf{1}}{\sqrt{\textbf{9}}}[/tex]
