An infinite series 8 x 64 x 512 x 4096 x 32768..... is multiplied by another infinite series 27 x 729 x 19683 x 531441..... . When cube rooted, the total will always be a product of......
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You might want to drop the word "infinite", since these "series" don't converge, and I doubt you're expecting us to work with supernatural numbers.