How do you multiply #(3 x 10^7)(5 x 10^4)#?

1 Answer
Mar 7, 2018

Answer:

See a solution process below:

Explanation:

First, rewrite the expression as:

#3 xx 10^7 xx 5 xx 10^4 =>#

#3 xx 5 xx 10^7 xx 10^4 =>#

#15 xx 10^7 xx 10^4#

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))#

#15 xx 10^color(red)(7) xx 10^color(blue)(4) =>#

#15 xx 10^(color(red)(7) + color(blue)(4)) =>#

#15 xx 10^11#

If it is necessary to write the solution in correct scientific notation we need to move the decimal point 1 place to the left so we need to add 1 to the 10s exponent:

#15 xx 10^11 =>#

#1.5 xx 10^12#