Question

$(81) {}^{ \frac{ - 1}{4} } \: \: \: \: \: \: \: \: evaluate$
​

Answer 1

Question :-

Evaluate :-

$\displaystyle\rm 81^{\frac{-1}{4}}$

Answer :-

$\displaystyle\rm (81)^{ - \frac{1}{4}}$

$\displaystyle\rm = \Bigg(\frac{1}{81} \Bigg)^ \frac{1}{4}$

$\displaystyle\rm = \Bigg(\frac{1}{3 \times 3 \times 3 \times3 }\Bigg)^ \frac{1}{4}$

$\displaystyle\rm = \Bigg(\frac{1}{ {3}^{4}} \Bigg) ^ \frac{1}{4}$

$\displaystyle\rm = \Bigg(\frac{ {1}^{4} }{3^{4} }\Bigg) ^{ \frac{1}{4} }$

$\displaystyle\rm = \frac{1}{ {( {3}^{ \cancel 4} })^ \frac{1}{\cancel 4} }$

$\displaystyle\rm = \frac{1}{3}$