Question

Please solve ASAP!
(⁴√9)(√9) ÷ ⁴√9⁵

Answer 1

`(\sqrt[4]{9})(√(9))/ \sqrt[4]{9^5}=\frac{\textbf{1}}{\sqrt{\textbf{9}}}`

Explanation:

Given expression is

`(\sqrt[4]{9})(√(9))/ \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* a^n=a^(m+n)`)

`=9^{\tfrac{3}{4}}* 9^{\tfrac{-5}{4}}` (by using the formulae
`{(a^m)}^n=a^(mn)` and
`(a^m)/(a^n)=a^(m-n)`)

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

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

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

`(\sqrt[4]{9})(√(9))/ \sqrt[4]{9^5}=\frac{\textbf{1}}{\sqrt{\textbf{9}}}`