That's been a trending topic in the frugal and prepper youtubes and blogs.
Uh...you can't cook without power. They mean without electricity. Since any time I cook at home is is WITHOUT ELECTRICITY I do not find this challenging.
Without "power" though...that's not a thing. It takes power to make heat and heat to cook. Ipso factoid: You need some type of power to cook.
Here are some of the not electric cooking methods I use all the freaking time and it is NOT a problem:
Wood...burn it. Put the food to be cooked close to the flame. Voila...cooked.
Butane...use a butane stove. Put the food to be cooked close to the flame. Voila...cooked.
Candles...use candles. Put the food to be cooked close to the flame. Voila...cooked. Use only small amounts of food for this one and thin pans because candles do not put out a huge amount of heat.
Solar...use the sun via a solar cooker (I have 3 types). Put the food to be cooked in the solar cooker. Voila...cooked.
Propane...use a propane stove or little heater burner. Put the food to be cooked close to the flame. Voila...cooked.