How do you simplify #\frac { 8.2\times 10^ { - 5} } { - 2\times 10^ { - 9} }#?

1 Answer
Mar 4, 2018

See a solution process below:

Explanation:

First, rewrite this expression as:

#8.2/-2 xx 10^-5/10^-9 =>#

#-4.1 xx 10^-5/10^-9#

We can now use this rule for exponents to simplify the 10s terms:

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

#-4.1 xx 10^color(red)(-5)/10^color(blue)(-9) =>#

#-4.1 xx 10^(color(red)(-5)-color(blue)(-9)) =>#

#-4.1 xx 10^(color(red)(-5)+color(blue)(9)) =>#

#-4.1 xx 10^4#

If we want to write this in standard form we need to move the decimal point 4 places to the right because the exponent of the 10s term is positive:

#-4.1 xx 10^4 = -41000#