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 22.
Any base raised to the power 0 is equal to 1 (20 = 1).
The base raised to the power of one is equal to the base (21 = 2)
When exponentials to the same base are multiplied, the exponent on the product is the sum of the exponents on the components.
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
When exponentials to the same base are divided, the exponent on the result is the exponent on the numerator minus the exponent of the denominator.
The example shows how exponents to different bases are combined oo division.
| 106 cm3 | = 106–4 cm3–2 = 102 cm (this is read one-hundred centimetres) |
| 104 cm2 |
Reversing the denominator and the numerator shows that exponents may also be negative.
| 104 cm2 | = 104–6 cm2–3 = 10–2 cm–1 (this is read 0.01 per centimetre) |
| 106 cm3 |