How do you simplify #(3.8 * 10 ^-5) ( 2.8 * 10 ^-5)# in scientific notation?

1 Answer
smendyka
Apr 11, 2018

See a solution process below:

Explanation:

First, rewrite this expression as:

#3.8 * 10^-5 * 2.8 * 10^-5 =>#

#3.8 * 2.8 * 10^-5 * 10^-5 =>#

#10.64 * 10^-5 * 10^-5#

Next, we can use this rule of exponents to multiply the 10s terms:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#10.64 * 10^color(red)(-5) * 10^color(blue)(-5) =>#

#10.64 * 10^(color(red)(-5)+(color(blue)(-5))) =>#

#10.64 * 10^(color(red)(-5)-color(blue)(5)) =>#

#10.64 * 10^-10#

To put this expression into scientific notation we need to move the decimal point 1 place to the left therefore we need to add #1# to the 10s exponent:

#10.64 * 10^-10 =>#

#1.064 * 10^(-10 + 1) =>#

#1.064 * 10^-9#

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