How do you calculate # (4 times 10 ^-3 )/(8 times 10^-7)#?

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Answer 1 · 2017-02-28T20:19:05

#5.0xx10^3#

#(color(blue)(4xx10^(-3)))/(color(red)(8xx10^(-7)))" "=" "color(blue)((4xxcolor(red)(10^7))/(color(red)(8)xx10^3) )#

#=4/8xx10^4#

#=0.5xx10^4#

As the question's format is of a particular style we should write our answer in the same format (scientific notation).

But written in scientific notation we need 5.0 and not 0.5

so we write #0.5# as #" "5.0xx1/10#

Putting it all together we have:

#5.0xx1/10xx10^4#

#5.0xx10^3#

Answer 2 · 2017-02-28T20:19:10

See the entire solution process below:

First, rewrite this expression as:

#(4/8)(10^-3/10^-7) = 0.5 xx (10^-3/10^-7)#

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))#

#0.5 xx (10^color(red)(-3)/10^color(blue)(-7)) = 0.5 xx x^(color(red)(-3)-color(blue)(-7)) = 0.5 xx 10^(color(red)(-3)+color(blue)(7)) =#

#0.5 xx 10^4#

Or

#5.0 xx 10^3#

Or

#5,000#