Negative exponents means the power(exponent) of a number is negative().If a number in numerator
having negative exponent is to be reciprocal by positive (i.e., a^{m} = 1/a^{m})
Let us try to solve few examples :

2^{3}
In the example 2^{3}, here exponent is negative i.e., 3 and we know that 2^{3} can be written as 2 x 2 x 2 we get 8. Now we can write 2^{3} as 1/2^{3} = 1/8
Therefore we get the result for 2^{3} as 1/2^{3}

3^{6}
In this example 3^{6}, here exponent is having negative number i.e., 6 and we know that 3^{6} can be written as 3 x 3 x 3 x 3 x 3 x 3, we get 729. Now we can write 3^{6} as 1/3^{6} = 1/729.
Therefore we get the result for 3^{6} as 1/3^{6}.
Let us try to solve few more examples :
Exponents 
Values 
Exponents 
Values 
2^{4} 
=16 
3^{4} 
= 81 
2^{3} 
=8 
3^{3} 
= 27 
2^{2} 
=4 
3^{2} 
= 9 
2^{1} 
=2 
3^{1} 
= 3 
2^{0} 
=1 
3^{0} 
= 1 
2^{1} 
= ? 
3^{1} 
= ? 
2^{2} 
= ? 
3^{2} 
= ? 
In the above table the exponents, i.e., 2^{4},2^{3},2^{2},2^{1},2^{0},2^{1},2^{2} are decreasing by 1, whereas values, i.e., 16,8,4,2,1 are decreasing by half. Following the same we get values of 2^{1} and 2^{2}.
By negative exponent 2^{1} = 1/2
Now 2^{2} = 1/2^{2} = 1/4
Coming to third column, the exponents, i.e., 3^{4},3^{3},3^{3},3^{2},3^{1},3^{0},3^{1<.sup>,32 are decreasing by 1, whereas values, i.e., 81,27,9,3,1 are decreasing by onethird. Following the same we get values of 31 and 32.}
By negative exponent 3^{1} = 1/3
and now 3^{2} = 1/3^{2} = 1/9
In the examples a^{n} = 1/a^{n} property is used. 
The examples have been illustrated in the video below :