What is (24^3)^-3 × (40÷4+14)^10 over (fraction bar) (96÷8)+(39÷3-1)

The answer is:  " 1 " .

Note:

(40 ÷ 4 + 14) ¹⁰ =  [ (40 ÷4) + 14 ] ¹⁰ = (10 + 14)¹⁰ = 24¹° ;

(96 ÷ 8) + (39 ÷ 3 −1 ) =  (96 ÷ 8) + [ (39 ÷ 3)  − 1 ] ;

                                    =    12 + (13  − 1 ) = 12 + 12  = 24 ;

  (24³)⁻³ = 24⁽³ * ⁻³⁾ = 24⁻⁹ ; 


So we can rewrite the problem:

24⁻⁹  *  (24¹⁰ / 24) ;  

Note:  " (24¹⁰ / 24) = (24¹⁰ / 24¹) = 24 ⁽¹⁰ ⁻ ¹⁾  =  24 ⁹ ;

Rewrite the expression:

 24⁻⁹  * 24 ⁹ = 24 ⁽⁻⁹ ⁺ ⁹⁾ = 24⁰ = 1 .

The answer is:  " 1 " .

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