Question

Please solve ASAP! (⁴√9)(√9) ÷ ⁴√9⁵

Answer 1

Answer:

$(\sqrt[4]{9})(\sqrt{9})\div \sqrt[4]{9^5}=\frac{\textbf{1}}{\sqrt{\textbf{9}}}$

Step-by-step explanation:

Given expression is

$(\sqrt[4]{9})(\sqrt{9})\div \sqrt[4]{9^5}$

The above expression can be written as

$\frac{(9)^{\tfrac{1}{4}}(9^{\tfrac{1}{2}})}{(9^5)^{\tfrac{1}{4}}}$

$=\frac{9^{\tfrac{1+2}{4}}}{9^{\tfrac{5}{4}}}$    (by using the formula $a^m\times a^n=a^{m+n}$)

$=9^{\tfrac{3}{4}}\times 9^{\tfrac{-5}{4}}$   (by using the formulae ${(a^m)}^n=a^{mn}$ and $\frac{a^m}{a^n}=a^{m-n}$)

$=9^{\tfrac{-2}{4}}$

$=9^{\tfrac{-1}{2}}$

$=\frac{1}{9^{\tfrac{1}{2}}}$

$(\sqrt[4]{9})(\sqrt{9})\div \sqrt[4]{9^5}=\frac{\textbf{1}}{\sqrt{\textbf{9}}}$