MATLAB: Convert cell array of character vectors to evaluable expressions

cell arraycharacter vectorMATLAB

I have a cell array of character vectors:
>> list
list =
  5×1 cell array
    {'10^{-4}'}
    {'10^{-3}'}
    {'10^{-2}'}
    {'10^{-1}'}
    {'10^{0}' }
I want to convert these vectors into the numbers they represent. I tried to use str2num, but it doesn't work with arrays or cell arrays. Using str2double, I get a cell array of NaNs because the character vectors are not only numbers, but rather expressions to evaluate. So I tried to use eval. This is my first attempt:
>> eval(list)
Error using eval
Must be a string scalar or character vector.
So I thought using cellfun would do the job because eval would be fed only one vector at a time, but instead I get this:
>> cellfun(eval, list)
Error using eval
Not enough input arguments.
After further tests, it seems like eval doesn't work with cellfun or arrayfun, which doesn't make sense to me. Is there any way to convert my expressions into numbers?

Best Answer

This is pretty easy with standard string parsing tools, e.g. sscanf:
>> C = {'10^{-4}';'10^{-3}';'10^{-2}';'10^{-1}';'10^{0}'};
>> V = sscanf([C{:}],'%d^{%d}');
>> Z = V(1:2:end).^V(2:2:end)
Z =
   0.00010000
   0.00100000
   0.01000000
   0.10000000
   1.00000000
You will find that this is quite fast too (1e4 iterations):
Elapsed time is 0.281599 seconds. % my answer
Elapsed time is 6.407189 seconds. % Fangjun Jiang's answer.
Also, because it does not use eval in any way (e.g. str2num), it is secure and does not impede MATLAB's JIT engine.
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