How to pronounce this dimension?
I need to say M^(-1) for my presentation, but cannot find an easy way to pronounce it? "M" here means "moles per liter". So in principle M^(-1) should be "moles per liter to the power of minus one". I wonder if there is an easier way to say it?

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It's pronounced "Em to the minus one".

Since M is said "molar", you could say "Molar to the minus one".
Of note, anything raised to the negative 1 power is simply its inverse, so M^-1 is actually 1/M, so "inverse molar" might also work.

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I'd use either Elvis's version, "to the power of negative one," or just "moles per litre to the negative one." It would be similar with Avogadro's constant (which I guess you are probably also using in your presentation): 6 x 10^23 would be "six times ten to the (power of) twenty-three."

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Use this dictionary to listen to the pronunciation, there are both British and American versions there: https://www.thefreedictionary.com

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To the power of negative 1*

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- Moles per litter, powered by minus one.