A binary operation

Algebra Level 1

Let \otimes be the binary operation such that a b = a b b a a \otimes b = a^b - b^a . What is the value of

3 4 ? 3 \otimes 4?


The answer is 17.

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19 solutions

It is the same as 3 4 4 3 3^4 - 4^3 which is equal to ( 3 2 × 3 2 ) ( 4 2 × 4 ) (3^2 \times 3^2) - (4^2 \times 4) so ( 9 × 9 ) ( 16 × 4 ) = 81 64 = 17 (9 \times 9) - (16 \times 4) = 81 - 64 = 17

Answer: 17 17

(9+8)(9-8)=17

Juang Bhakti Hastyadi - 7 years, 9 months ago

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Nice factorization! Love this observation which avoids having to multiply out all the numbers.

Calvin Lin Staff - 7 years, 9 months ago
Anubhav Mishra
Aug 29, 2013

3^4 -4^3

=81-64

=17

3 4 3\bigotimes4

= 3 4 4 3 =3^4-4^3

= 17 =17

Joshua Crouch
Aug 26, 2013

3 3 3*3=81

4 4 4=64

81-64=17

Tarek Saazeb
Aug 25, 2013

3^4 - 4^3 = 81 - 64 = 17

Vineet Advani
Sep 1, 2013

3^4 - 4^3 = 81 - 64

81 - 64 = 17

Nishant Singh
Aug 30, 2013

(3^4)-(4^3)= 81-64 = 17

Talha Naveed
Aug 30, 2013

(3^4) - (4^3)

= 81 - 64

= 17

Siti Zulhusna
Aug 30, 2013

3^4 - 4^3 = 17

Joseph Doroy
Aug 30, 2013

3^4-4^3=3 3 3 3-4 4*4=81-64=17

Henry Okafor
Aug 30, 2013

3⊗4= 3 4 3^{4} - 4 3 4^{3} =81-64=17

Kho Yen Hong
Aug 29, 2013

3X4=3^4 - 4^3=9^2 - 8^2=(9-8)(9+8)=17

Basem Hesham
Aug 27, 2013

a⊗b=a^b−b^a then >>> 3⊗4 means 3^4-4^3 = 17 answer is =17

Daniel Chiverton
Aug 27, 2013

3^4=81 4^3=64 81-64=17

Elias Alves
Aug 27, 2013

3 x 4=3.3.3.3 - 4.4.4 3 x 4=81 - 64 3 x 4 = 17 Resultado 17

Eugene Novela
Aug 27, 2013

3⊗4=3^4-4^3=81-64=17 To make it clarified: The symbol (^) represents an exponent. FOR THE LONG METHOD: 3⊗4=3 3 3 3-4 4*4 =81-64 =17

Sana Irfan
Aug 26, 2013

3^4 * 4^3=81-64=17

hey i'd also done like that

shashwat sam - 7 years, 9 months ago

3^4 - 4^3 = 81-64 = 17

Anna Ruth Alvarez - 7 years, 9 months ago
Chengfang Goh
Aug 26, 2013

3^4 - 4^3 = 81 - 64 =17

Rakhmat Muliawan
Aug 25, 2013

3 ⊗ 4 = 3^4 - 4^3 = 81 - 64 = 17

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