A number to the first power is that number one time, or simply that number: for
example, 6^{1} = 6 and 53^{1} = 53. We define a number to
the zero power as 1: 8^{0} = 1, ( 17)^{0} = 1, and
521^{0} = 1.
Here is a list of the powers of two:
2^{0}  =  1 

2^{1}  =  2 

2^{2}  =  2×2 = 4 

2^{3}  =  2×2×2 = 8 

2^{4}  =  2×2×2×2 = 16 

2^{5}  =  2×2×2×2×2 = 32 

and so on...
Exponents and the Base Ten System
Here is a list of the powers of ten:
10^{0}  =  1 

10^{1}  =  10 

10^{2}  =  10×10 = 100 

10^{3}  =  10×10×10 = 1, 000 

10^{4}  =  10×10×10×10 = 10, 000 

10^{5}  =  10×10×10×10×10 = 100, 000 

and so on...
Look familiar? 10^{0} is 1 one (a 1 in the ones place), 10^{1}
is 1 ten (a 1 in the tens place), 10^{2} is 1 hundred, 10^{3} is
1 thousand, 10^{4} is 1 ten thousand, etc. This is the meaning of
base tena "1" in each place represents a
number in which the base is 10 and the exponent is the number of zeros after the
1. The place value is the number that is multiplied by this number. For
example, a 5 in the thousands place is equivalent to 5×1000, or
5×10^{3}.
We can write out any number as a sum of singledigit numbers times powers of
ten. The number 492 has a 4 in the hundreds place (4×10^{2}), a 9 in
the tens place (9×10^{1}) and a 2 in the ones place (2×10^{0}).
Thus, 492 = 4×10^{2} +9×10^{1} +2×10^{0}.
Examples: Write out the following numbers as singledigit numbers times
powers of ten.
935 = 9×10^{2} +3×10^{1} +5×10^{0}
67, 128 = 6×10^{4} +7×10^{3} +1×10^{2} +2×10^{1} +8×10^{0}
4, 040 = 4×10^{3} +0×10^{2} +4×10^{1} +0×10^{0}