There is no Adapter to switch them the _USA power supply is rated at 120v@60hz while Singapore is 230v@50hz with a 10amp fuse_ you will have to purchase a seperate power supple to supply that can support the power outlets that are supplied by your country.
Important Microsoft does not license any non-Microsoft accessories that plug into the Xbox console's power socket. Use of any accessory other than the standard Xbox 360 power supply may damage your console and void your console warranty.
PSUs are designed to be used only in the regions where they are sold.
Don't try to use an Xbox 360 power supply that was built for a region that has different power requirements.
Don't use an unlicensed accessory, such as a non-Microsoft replacement power supply or any accessory that plugs in between the Xbox 360 console and the power supply.
Don't use the Xbox 360 external power supply outside the country where the power supply was sold. If you use the power supply in a different country, the power supply or your Xbox 360 console may be damaged, and the warranty may be invalidated.
The Xbox 360 power supply contains an internal fuse that helps protect your console from too-high voltage and power surges. However, the PSU is a sealed unit. Therefore, you cannot replace the internal fuse. The power supply is rated for of 245 watts of
continuous power and 280 watts of maximum power.
Source:
support.xbox.com/.../power-supply
Where to buy it is a hard question and you should probably get on a live chat with Microsoft/Xbox support (link below) and ask them where Microsoft/Xbox certified dealers/markets in Singapore are located, and when you find this out you will probably
be able to buy one directly from them, and make sure to use a Microsoft made non third part PSU as this could lead to the damage and voided warranty of your Xbox360 console, I wish best of luck to you with your problem it looks like a very tricky one.
Xbox Live Chat Live Support:
support.xbox.com/.../contact-us