If x is negative, then we apply the property of exponents, a -m = 1/a m and then we apply the same logic as explained earlier. If x is positive, we simplify 10 x by multiplying 10 by itself x times. The powers of 10 are of the form 10 x, where x is an integer. This means that we need to multiply 10 seven times, that is, 10 7 = 10 × 10 × 10 × 10 × 10 × 10 × 10

For example, 10 to the 7th power means 10 7. Now, let us try to understand it the other way round. Here, 10 is the base and 9 is the power and this is read as 10 to the ninth power. Therefore, exponents help to express this easily and this value (10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 1000000000) can be expressed as 10 9. Now, if we need to multiply 10 thirty times, it would be even more difficult to write the product with so many zeros. If we multiply 10 a couple of times it becomes difficult to write the number as in this case, 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 1000000000. These numbers which are written as exponents are the powers of 10. The following example shows the same quantity written in different ways.The powers of 10 means when 10 is multiplied a certain number of times, the product can be expressed using exponents. Prefixes are easier to write and pronounce than powers of 10. These are referred to as regular prefixes and may be used with any SI unit. Most of the prefixes in the table above are multiples of a thousand. ‘Kilo’ comes from the Greek word for 1000 (10 3), and ‘milli’ comes from the Latin word for one thousandth (10 -3). Prefix names have been mostly chosen from Greek words (positive powers of 10) or Latin words (negative powers of 10), although recent extensions of the range of powers of 10 has resulted in the use of words from other languages. For example, where does ‘kilo’ come from? To many people, the choice of prefix names seems strange. Using the prefix for 10 9 from the table above, this becomes 78 Gm, which is pronounced as ‘seventy-eight gigametres’. The distance from the Earth to Mars is 78 million kilometres, which is 78 x 10 6 km, and this in turn is 78 x 10 9 m. The ‘km’ means kilometre, which is 10 3 m. For example, in the article Distances in space, it states: When the Space Shuttle goes into space, it orbits about 700 km above the surface of the Earth. The Space revealed resources deal with extremely large distances.In abbreviated form, this length is written as 1 nm. In the Nanoscience resources, it is reported that fingernails grow at about 1 nanometre per second.In abbreviated form, this amount of energy is written as 25 mJ. One unit on the UV index is roughly equivalent to 25 millijoules of UV energy falling per second on a 1 square metre area. In the You, Me and UV resources, information is given about the UV index.The first letter of the SI abbreviation represents the prefix and the second letter represents the base unit.

These prefixes are decimal fractions that multiply base units for smaller measurements These prefixes multiply base units for larger measurements For small lengths, the millimetre (10 -3 m) may be the appropriate quantity, whereas for large distances, the kilometre (10 3 m) may be more appropriate. For example, the base unit of length is the metre. Larger and smaller quantities are expressed by using appropriate prefixes with the base unit.

they eliminate the confusion of old number names – is a billion a thousand million (USA) or a million million (Europe)?.they are unique, unambiguous letter symbols.there are no long rows of zeros – prefixes replace them.The advantages of basing the multiples and submultiples on the decimal system are:

The power of ten show