How do you write the answer in scientific notation given #(4.5times10^4)^2#?

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Answer 1 · 2017-05-18T01:23:37

See a solution process below:

We can rewrite the expression as:

#(4.5 xx 10^4)(4.5 xx 10^4) => (4.5 xx 4.5)(10^4 xx 10^4) =>#

#20.25 xx ((10^4 xx 10^4)#

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

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

#20.25 xx (10^color(red)(4) xx 10^color(blue)(4)) => 20.25 xx 10^(color(red)(4) + color(blue)(4)) => 20.25 xx 10^8#

Now, we need to move the decimal point 1 place to the left to change this to true scientific notation:

#20.25 xx 10^8 => 2.025 xx 10^9#