Positive exponents are a shorthand way of indicating how many times a base is multiplied by itself.
The base can be a number, a variable (like the letter
x) or a unit (like cm for centimetre).
The exponent is sometimes referred to as a power, for example 2 raised to the power 2 is equal to 2
2. 22 = 2 × 2
21 = 2
20 = 1 | x4 = x × x × x × x
x1 = x
x0 = 1 | cm3 = cm × cm × cm
cm1 = cm
cm0 = 1 |
As is also shown above:
Any base raised to the power 0 is equal to 1.
The base is equal to the base raised to the power of 1.
When exponentials to the same base are multiplied, the exponent on the product is the sum of the exponents on the components.
cm1 × cm1 × cm1 = cm1+1+1 = cm3
In the example above each of the numbers is a measurement, and a measurement is a number (in this case a power of 10) times its unit.
When these are multiplied any products that are to the same base can be combined as above.
102 cm × 10 cm × 103 cm = 102+1+3 cm1+1+1 = 106 cm3