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

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

2 votes
The answer is: " 1 " .
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Note:
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(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 ;
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(24³)⁻³ = 24⁽³ * ⁻³⁾ = 24⁻⁹ ;

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So we can rewrite the problem:
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24⁻⁹ * (24¹⁰ / 24) ;
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Note: " (24¹⁰ / 24) = (24¹⁰ / 24¹) = 24 ⁽¹⁰ ⁻ ¹⁾ = 24 ⁹ ;
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Rewrite the expression:
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24⁻⁹ * 24 ⁹ = 24 ⁽⁻⁹ ⁺ ⁹⁾ = 24⁰ = 1 .
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The answer is: " 1 " .
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User Ed McManus
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