Question

What is the simplified value of $(81{)}^{\frac{-1}{4}}$ $+(81{)}^{\frac{1}{4}}?$

Answer 1

$(81{)}^{\frac{-1}{4}}$ $+(81{)}^{\frac{1}{4}}=(3^4{)}^{-\frac{1}{4}}+(3^4{)}^{\frac{1}{4}}$
$=(3{)}^{4\times -\frac{1}{4}}+(3{)}^{\frac{1}{4}\times 4}$ [Since, $(a^m{)}^n=a^{m\times n}$]
$=3^{-1}+3$
$=3+\frac{1}{3}$ [Since, $a^{-m}=\frac{1}{a^m}$]
$=\frac{9+1}{3}$
$=\frac{10}{3}$
Hence, the value of the given expression is $\frac{10}{3}$