How do you evaluate #\frac { ( 3.00\times 10^ { 6} ) ( 2.0\times 10^ { - 3} ) } { 5.0\times 10^ { - 2} }#?

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Answer 1 · 2016-12-10T14:33:27

#120,000# or #1.2 xx 10^5#

First, rearrange the terms in the numerator:

#(3.00 xx 2.0 xx 10^6 xx 10^-3)/(5.00 xx 10^-2)#

Using the rule for exponents where #color(red)(x^a xx x^b = x^(a+b))# we can simplify the numerator to:

#(6.00 xx 10^(6-3))/(5.0 xx 10^-2)#

#(6.00 xx 10^3)/(5.0 xx 10^-2)#

Now using the rule for exponents where #color(red)(x^a/x^b = x^(a-b))# we can simplify the fraction to:

#(6.00 xx 10^((3 - -2)))/5.0#

#(6.00 xx 10^5)/5.00#

Expanding the numerator gives us:

#600000/5#

#120000#

#1.2 xx 10^5#

Answer 2 · 2016-12-10T14:35:32

#1.2 * 10^5#

#((3.00 * 10^6)(2.0 * 10^-3))/(5.0 * 10^-2#

multiply out brackets:

#(6.0 * 10^3)/(5.0 * 10^-2)#

divide 6 by 5:

#(1.2 * 10^3)/10^-2#

and then the powers of 10:

#1.2 * 10^5#

(reason:) law of indices:
#(a^m/a^n = a^(m-n))#

#1.2# is between 1 and 10, so we do not need to change this or the power of 10.

final answer: #1.2 * 10^5#