It will be fine. HP sells a computer named X51 which only has 330w of power and comes with a GTX 670 (Which uses more power then the Radeon 7870) and people even put a GTX 680 in it (Even more power) 500W (or greater) power supply with one 75W 6-pin PCI Express power connector recommended
600W power supply (or greater) with four 75W 6-pin PCI Express power connectors recommended for AMD CrossFire™ technology.
NOTE: Minimum recommended system power supply wattage is based on the specific graphics card and the typical power requirements of other system components. Your system may require more or less power. OEM and other pre-assembled PCs may have different power requirements.