The answer is yes, but there are certain restrictions that need to be taken into account. It is allowed to carry power banks in your cabin luggage, but not in your checked-in luggage.
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Lithium-ion (rechargeable) batteries and portable batteries that contain lithium-ion can only be packed in carry-on baggage. They're limited to a rating of 100 watt hours (Wh) per battery. With airline approval, you can bring two larger spare batteries (up to 160 Wh).
Maximum capacity: 100 Wh or 27000 mAh. Emirates — spare or extra batteries (including lithium and lithium-ion batteries) can only be carried in carry-on luggage. Items that mainly serve as an energy source (e.g. power banks), are considered spare batteries. There is a limit of 20 spare batteries per passenger.
Powerbanks restrictions are airline specific. Most allow only up to 10000mAh only in the carry-on luggage. You are not allowed to put them in your checked baggage. That being said, I have flown in and out of Singapore with power banks and had no issues either way.
The reason behind this is that power banks contain lithium-ion batteries, which are considered dangerous goods by the International Air Transport Association (IATA). Lithium-ion batteries have a high energy density and, if not handled correctly, they can pose a risk of fire or explosion.
Power banks cannot be check-in and must be carried in hand luggage. The battery limit is 100Wh, so it depends on the voltage of the power bank as well. Most power banks are 5V. A 10000mAh x 5V battery is 50Wh which is well within the limit.
Spare (uninstalled) lithium metal batteries and lithium ion batteries, electronic cigarettes and vaping devices are prohibited in checked baggage. They must be carried with the passenger in carry-on baggage.
You can take all plug-in phone chargers with you in your carry-on or checked bags with ease as they do not contain any form of battery and, therefore, do not present any danger. Typically, you will not be able to use this type of charger onboard as most airplanes do not have power sockets.
Portable chargers or power banks containing a lithium ion battery must be packed in carry-on bags. For more information, see the FAA guidance on portable rechargers.
The rules on a piece of paper handed over by the security stated that you can only carry on if it is clearly marked with value <20000mAH x 5V or < 100wH. For those between 20000mAH to 32000mAH (100wH - 160wH) you have to declare and check in. Actually the rating allowed is very high, most powerbanks are much lower!