How do you add, subtract, divide, and multiply scientific notation expressions

Scientific notation is
n*10^x
where 1≤n<10 and x is a whole power
so remember some simple rules
(ab)(cd)=(a)(b)(c)(d)=(ac)(bd)

also properties of exponents

and


why is this important?

because
lets say
8*10^9 times 4*10^2
this means
(8)(10^9)(4)(10^2)=(8*4)(10^9*10^2)=32*10^{9+2}=32*10^11, but wait, it has to be less than 10
32=3.2*10^1
32*10^11=3.2*10^1*10^11=3.2*10^12

for division
=1.5*10^5

the only way to add or subtract scientifict notation is when the x on the 10^x are the same
otherwise, yo have to expand the expressions

Sin(a)+cos(a)+cot(a)-1=2(csc(x)+1)