Question

(46656)⁻¹/⁶, Solve this expression?

Answer 1

we have (46656)^-1/6= (6)^6×-1/6 = 6^-1=
1/6 ans.

Answer 2

Given ( 46656 )^-1/6

Solution :

Prime factors of 46656

2 | 46656

_________

2 | 23328

__________

2 | 11664

__________

2 | 5832

__________

2 | 2916

__________

2 | 1458

__________

3 | 729

__________

3 | 243

__________

3 | 81

__________

3 | 27

__________

3 | 9

__________

*****3

46656 = 2^6 × 3^6

= ( 2 × 3 )^6

= ( 12 )^6

Now ,

( 46656 )^-1/6

= 1/( 46656 )^6

[ Since , a^-m = 1/a^m ]

= 1/[ ( 12^6 )]^1/6

= 1/[ 12^6/6 ]

[ Since ( a^m )^n = a^mn ]

= 1/12

Therefore ,

( 46656 )^-1/6 = 1/12

Or ( 12 )^-1

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