Simplifying an arithmetic expression written using scientific notation.

Hey, so. I need a problem worked out that uses Newton's gravitational constant.(If you dont want to read this, skip to the problem below) And, I have to present it to the class tommorrow.. I can punch it into a calculator just fine and do it when the exponets are gone (the problem is in scientific notation) BUT.. Since it will be explained to the class on a board, I want to leave the problem in scientific notation until the very end. I know the answer. N= 686. But I keep getting a different answer. Very frustrating.Im sure Im just making a small error. Anyway Problem is:

(6.673 x 10-11 N m2/kg2) x (5.98 x 1024 kg ) x (70 kg)

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(6.38 x 10^6 m)^2

Whats used is Gravitation constant times mass of one times mass of two over distance squared.

So yeah, theres a way to multiply/divide and keep it in scientific notation, can someone please show a step by step how-to? Much appreciated.thanks.