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This stuff is tricky. Saying just how you say things that no one would say in any case, is hard.
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> or <math>(x^2)^2</math> is the second component squared.
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