How do you simplify #(5 times 10^7)(9 times 10^-3) / (3 times 10^-2)# in scientific notation?

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Answer 1 · 2015-11-20T11:07:01

#15*10^6#

First of all, since the multiplication is commutative, you can deal with numbers and powers of ten separately:

#5 times 10^7 \frac{9 times 10^{-3}}{3 times 10^{-2}} = 5* 9/3 times 10^7 \frac{10^{-3}}{10^{-2}#

Of course, #5 * 9/3 = 5*3 = 15#.

As for the powers of ten, remember that

#a^b * a^c = a^{b+c}#, and #a^b/a^c = a^{b-c}#

This means that

#10^7 \frac{10^{-3}}{10^{-2}} = 10^{7-3-(-2)}=10^{7-3+2}=10^6#