How do you multiply #( 7.4\times 10^ { - 3} ) ( 9.32\times 10^ { - 8} )#?

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Answer 1 · 2017-05-06T12:40:05

#6.8968 xx 10^-10#

See the solution process below:

First, rewrite the expression as:

#(7.4 xx 9.32)(10^-3 xx 10 ^-8) => 68.968 xx (10^-3 xx 10 ^-8)#

We can now use this rule of exponents to multiply the powers of 10.

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

#68.968 xx (10^color(red)(-3) xx 10^color(blue)(-8)) => 68.968 xx 10^(color(red)(-3) + (color(blue)(-8)) =>#

#68.968 xx 10^-11#

Or, to put the expression into correct scientific notation:

#6.8968 xx 10^-10#