how to solve the product of unit digit {(345^567)*(454^675)*(5678^6754)*(6789^789)}

I need to know wht should we do to solve the question nin short time
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?????????? "yunit digit" ?????????? yu gotta hav software that kan handel unlimited number digits... 345^567=87,786,332,684,398,098,641,135,018,556,751,775,490.... hav 1439 digits just for this much, me kant even rite all that heer... & then yu wanna multipli 4 even bigger numbers tugether???????
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