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A number to the first power is that number one time, or simply that number: for example, 61 = 6 and 531 = 53. We define a number to the zero power as 1: 80 = 1, (- 17)0 = 1, and 5210 = 1.

Here is a list of the powers of two:


20=1  
21=2  
22=2×2 = 4  
23=2×2×2 = 8  
24=2×2×2×2 = 16  
25=2×2×2×2×2 = 32  


and so on...

Exponents and the Base Ten System

Here is a list of the powers of ten:


100=1  
101=10  
102=10×10 = 100  
103=10×10×10 = 1, 000  
104=10×10×10×10 = 10, 000  
105=10×10×10×10×10 = 100, 000  


and so on...

Look familiar? 100 is 1 one (a 1 in the ones place), 101 is 1 ten (a 1 in the tens place), 102 is 1 hundred, 103 is 1 thousand, 104 is 1 ten thousand, etc. This is the meaning of base ten--a "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 5×103.

We can write out any number as a sum of single-digit numbers times powers of ten. The number 492 has a 4 in the hundreds place (4×102), a 9 in the tens place (9×101) and a 2 in the ones place (2×100). Thus, 492 = 4×102 +9×101 +2×100.


Examples: Write out the following numbers as single-digit numbers times powers of ten.

935 = 9×102 +3×101 +5×100
67, 128 = 6×104 +7×103 +1×102 +2×101 +8×100
4, 040 = 4×103 +0×102 +4×101 +0×100

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