Question

evaluate this question of indices ​

Answer 1

Answer:

we know that , ( a / b ) ^n = a^ n / b^ n ( by laws of exponents ).

Here , a = 8 ^ 1 / 2 and b = 9 ^ ( - 3 ) and n = 1 / 6

Hence , it is equal to

FOR THE NUMERATOR

=> 8 ^ 2/ 6 = 8 ^ 1 /3 = 2 ( cube root of 8 = 2) ;

FOR THE DENOMINATOR

=> 9 ^ ( -3) / 6 = 9 ^ ( -2 ) = 3 ( square root of 9 = 3) ;

Hence , fraction = 2 / 3.

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