How do you write the answer in scientific notation given #(1.2times10^-4)^2/((9.0times10^5)(1.6times10^-8))#?

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Answer 1 · 2017-10-14T13:01:19

#1.0xx10^-6#

First we need to remember three properties of exponents:
1) #(A*B)^x=A^x*B^x#
2) #A^-x=1/A^x#
3) #A^x*A^y=A^(x+y)#

Using the first property on the top leaves us with:
#1.2^2xx(10^-4)^2#

Now, when you have an exponent raised to an exponent you multiply them, in this case getting #10^-8#. Now our full equation looks like this:

#(1.44xx10^-8)/((9.0xx10^5)xx(1.6xx10^-8))#

We can eliminate both #10^-8#'s from the top and bottom:

#1.44/((9.0xx10^5)xx1.6)#

If we divide top and bottom by 2, 4 times, we get:

#1.44 div 2=0.72 div 2=0.36 div 2=0.18 div 2=0.09" "# on top

and

#1.6 div 2=0.8 div 2=0.4 div 2=0.2 div 2=0.1" "# on the bottom,

leaving our equation like this:

#0.09/((9.0xx10^5)xx0.1)#

Now, we divide #0.09# by #0.1# leaving us #0.9# on top

#0.9/(9.0xx10^5)#

Divide top and bottom by 9

#0.1/(1.0xx10^5)#

#0.1# can also be written as #1.0xx10^-1#

#(1.0xx10^-1)/(1.0xx10^5)#

and using the second property we can write:

#(1.0xx10^-1)xx(1.0xx10^-5)#

Finally we can throw out the parenthesis and use the third property, adding the exponents on the 10's, leaving us with the final number:

#1.0xx10^-6#