How do you evaluate #(0.8\times 10^ { 4} ) ( 128\times 10^ { 4} )#?

1 Answer
smendyka
Sep 29, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

#(0.8 xx 128) xx (10^4 xx 10^4) =>#

#102.4 xx (10^4 xx 10^4)#

Now, 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))#

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

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

#102.4 xx 10^8#

If we want to write this in standard scientific notation we need to move the decimal point 2 places to the left which means we need to increase the exponent of the 10s term:

#102.4 xx 10^8 => 1.024 xx 10^10#

If we want to right this in standard notation we need to move the decimal point 10 places to the right:

#1.024 xx 10^10 => 10,240,000,000#

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