How do you simplify #\frac { 8\cdot 10^ { 7} } { 4\cdot 10^ { 6} }#?

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Answer 1 · 2017-05-06T01:29:13

See a solution process below:

First, rewrite this expression as:

#(8/4)(10^7/10^6) => 2(10^7/10^6)#

Now, use this rule of exponents to simplify the 10s terms:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#2(10^color(red)(7)/10^color(blue)(6)) => 2 * 10^(color(red)(7)-color(blue)(6)) => 2 * 10^1#

If we want to simplify further we can use this rule of exponents:

#a^color(red)(1) = a#

#2 * 10^color(red)(1) = 2 * 10 = 20#