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So, the components of the above vector could be written <math>\vec{\boldsymbol{x}}=(x^1,x^2,x^3)</math>.

So, the components of the above vector could be written <math>\vec{\boldsymbol{x}}=(x^1,x^2,x^3)</math>.

But doesn't writing the vector components as superscripts lead to ambiguity with raising something to a power?  Not really.  Proper tensor vector equations '''almost never raise a vector component to a power.'''  When one must do so, the convention is to put the power in parentheses.  So <math>x^2</math> is the second component of a vector, <math>x^{(2)}</math> is the number x squared, and <math>x^{2^{(2)}}</math> is the second component squared.

But doesn't writing the vector components as superscripts lead to ambiguity with raising something to a power?  Not really.  Proper tensor/vector equations '''almost never raise a vector component to a power.'''  When one must do so, the convention is to put the power in parentheses.  So <math>x^2</math> is the second component of a vector, <math>x^{(2)}</math> is the number x squared, and <math>x^{2^{(2)}}</math> is the second component squared.

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