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−  == Problem ==
 +  #redirect [[2006 AMC 12A Problems/Problem 2]] 
−  Define <math>x\otimes y=x^3y</math>. What is <math>h\otimes (h\otimes h)</math>?
 
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−  <math> \mathrm{(A) \ } h\qquad \mathrm{(B) \ } 0\qquad \mathrm{(C) \ } h\qquad \mathrm{(D) \ } 2h\qquad \mathrm{(E) \ } h^3 </math>
 
−  == Solution ==
 
−  Plugging our values into the defined [[operation]], we have
 
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−  <center><math>\displaystyle h\otimes h = h^3h</math></center>
 
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−  Plugging in the [[function]] once more, we have
 
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−  <center><math>\displaystyle h\otimes(h\otimes h) = h\otimes (h^3  h) = h^3(h^3h)=h</math></center>
 
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−  which is choice <math>(C)</math>.
 
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−  == See also ==
 
−  {{AMC10 boxyear=2006ab=Anumb=1numa=3}}
 
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−  [[Category:Introductory Algebra Problems]]
 