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  • The value of 4sqroot(81)power -2 is : (A)1 by 9(B)1by3(C) 9 (D)1 by 81

The value of \sqrt[4]{\left ( 81 \right )^{-2}}is :

(A)\frac{1}{9}
(B)\frac{1}{3}
(C)9
(D)\frac{1}{81}

Answers (1)

Answer.     [A]
Solution.        

We have, \sqrt[4]{\left ( 81 \right )^{-2}}
We know that \sqrt[n]{a}= \left ( a \right )^{\frac{1}{n}}
So,
\sqrt[4]{\left ( 81 \right )^{-2}}= \left ( \left ( 81 \right )^{-2} \right )^{\frac{1}{4}}    

=\left ( 81 \right )^{-2\times \frac{1}{4}}                    \because \left ( a^{m} \right )^{n}= a^{m\times n}       

= 81^{-\frac{1}{2}}= \left ( \frac{1}{81} \right )^{\frac{1}{2}}            \because \left ( a^{-m}= \left ( \frac{1}{a} \right )^{m} \right )                                     

= \sqrt{\frac{1}{81}}
=\frac{1}{9}                                                       

Hence option A is correct

Posted by

infoexpert27

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