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# Module 1 - Introduction to Matter, Energy, and Direct CurrentNavy Electricity and Electronics Training Series (NEETS)Chapter 3:  Pages AII-1 through AII-3

APPENDIX II

LAWS OF EXPONENTS

The International Symbols Committee has adopted prefixes for denoting decimal multiples of units. The National Bureau of Standards has followed the recommendations of this committee, and has adopted the following list of prefixes:

 Numbers Powers of ten Prefixes Symbols 1,000,000,000,000 1012 tera T 1,000,000,000 109 giga G 1,000,000 106 mega M 1,000 103 kilo k 100 102 hecto h 10 10 deka da .1 10-1 deci d .01 10-2 centi c .001 10-3 milli m .000001 10-6 micro u .000000001 10-9 nano n .000000000001 10-12 Pico p .000000000000001 10-15 femto F .000000000000000001 10-18 atto a

To multiply like (with same base) exponential quantities, add the exponents. In the language of algebra the rule is am x an  = am+n

AII-1

To divide exponential quantities, subtract the exponents. In the language of algebra the rule is

*Generally used with electrical quantities.

To raise an exponential quantity to a power, multiply the exponents. In the language of algebra
(xm)n  = xmn.

Any number (except zero) raised to the zero power is one. In the language of algebra xO  = 1

Any base with a negative exponent is equal to 1 divided by the base with an equal positive exponent. In the language of algebra x-a  = 1/xa

To raise a product to a power, raise each factor of the product to that power.

AII-2

To find the nth root of an exponential quantity, divide the exponent by the index of the root. Thus, the nth root of am = am/n.

AII-3