Does 970 chipset motherboards support amd am3+ 9370 and 9590 cpus ??? No, none do.
The ASRock Fatal1ty 990FX Professional and 990FX Extreme9 support AMD FX-9370 and FX-9590 220W Desktop Processor. ASRock 990FX Extreme3 has no support for those 220 watt TDP CPUs.
GIGABYTE GA-990FXA-UD3 (latest rev 4) not 990XA-UD3 support those 220 watt TDP CPUs.
You should always refer to the motherboard manufacturers CPU Support List for compatible CPUs. The required BIOS version will also be listed.