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

Question

Eva Adamson · Accepted Answer

See a solution process below:

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#

Avery Alexander · Answer

undefined To simplify (3.8 * 10^-5) * (2.8 * 10^-5) in scientific notation, you multiply the coefficients (3.8 * 2.8) and add the exponents (-5 + -5).

The result is 10^(-10) multiplied by 10.64, which simplifies to 1.064 * 10^(-9) in scientific notation.