Question

${[1-{\{1-{(1-a^4)}^{-1}\}}^{-1}]}^{-\frac{1}{4}}$ is equal to

• A. $a^4$
• B. $a^2$
• C. $a$
• D. $\frac{1}{a}$

Answer 1

Answer: (C)

$a$

Given exp $={[1-{\{1-\frac{1}{1-a^4}\}}^{-1}]}^{-\frac{1}{4}}$
$={[1-{\left\{\frac{1-a^4-1}{1-a^4}\right\}}^{-1}]}^{-\frac{1}{4}}$
$={[1-{\left\{\frac{-a^4}{1-a^4}\right\}}^{-1}]}^{-\frac{1}{4}}={[1-\left\{\frac{1-a^4}{-a^4}\right\}]}^{-\frac{1}{4}}$
$={[1-\left\{\frac{a^4-1}{a^4}\right\}]}^{-\frac{1}{4}}={\left[\frac{a^4-a^4+1}{a^4}\right]}^{-\frac{1}{4}}$
$={\left(\frac{1}{a^4}\right)}^{-\frac{1}{4}}=(a^{-4}{)}^{-\frac{1}{4}}=a^1=a$