What you are saying about change to implicit-expansion makes sense. I can accept that.

I did try bsxfun already. For some reason it seemed to be slower than just using a for loop. 

FOR LOOP Construction:

A = nan(size(u,1), size(exponent,1));

for i = 1:n
    A(:,i) = u(:,1).^(exponents(i,1));
end

bsxfun Construction:

A = bsxfun(@power, u(:,1), exponents(:,1)');