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What is Exponents ? 
When a number is written in the form of aⁿ, the number is said to written in the exponential form.  Here a is called the base of the number and n is called the power or exponents.. For example 3⁸ Here 3 is the base and 8 is the exponents.

Multiplicative Inverse
For non- zero integer a , a^-m = 1/a^m, where m is a positive integer.
And  a^-m is called the multiplicative inverse of  a^m .

Laws of Exponents 

For any non zero integer a and integer m and n, the laws of exponents are 

1. ^{am x an = am+n} 
2. a^m/aⁿ = a^m-n
3. (a^m)ⁿ = a^mn
4. a^m x b^m = (ab)^m
5. a^m/b^m = (a/b)^m
6  (a^-m) = 1/a^m
7  a⁰ = 1

So according to laws 
if (2)^-3 = (1/2)³ =1 / 8
if (1/3)^-3 = (3/1)³ = 27
if (-3)⁴ x (-3)^-12 = (-3) ^4-12 = (-3)^-8 = (1/-3)⁸

Some More examples
Proof 
1.  (a + b)^-1 (a^-1 + b^-1) = (ab)^-1
L.H.S = (a + b)^-1 (a^-1 + b^-1)
         =  1 /(a +b) [1/a + 1/b]
         = 1/(a + b) [(b + a)/ab]
         = 1/(a + b) x (a + b)/ab 
         = 1/ab  = (ab)^-1 = R.H.S   

Simplify
[ 2^-1 + 3⁰ + 5¹ + 7² + 9³]  x (2/3)
= [1/2 + 1 + 5 + 49 + 729] x (2/3)
= [1/2 + 784] x (2/3)
= (1569/2) x (2/3)
= 1569/3 
= 523

Solution :-
1.  0.0000000003904 = 3.904 x 10^-10