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# Arithmetic : Exponents, Powers and Roots of Numbers

 Preparation Just what you need to know !

Exponents

The power n is called the exponent and a is called the base in an.
For example in 74, 4 is the exponent and 7 is the base.

The rules or laws of exponents are:

 MUST-KNOW: Rule 1 : an × am = an + m Rule 2 : an × bn = (a b)n Rule 3 : (an)m = anm

Here, a and b are any numbers, and n and m are any positive integers or zero.

Consider the following examples:

Rule 1 : 22 × 25 = 4 × 32 = 128 and 22 × 25 = 27 = 128
Rule 2 : 23 × 43 = 8 × 64 = 512 and 23 × 43 = 83 = 512
Rule 3 : (32)3 = 93 = 729 and (32)3 = 36 = 729

If n is a positive integer, then a negative exponent is defined as

MUST-KNOW : a−n = 1/an

This is obtained from the first law of exponents as follows:
a−n × an = a−n + n = a0 = 1, so a−n = 1/an.
For example, 2−4 = 1/24 = 1/16 and (¼)−1 = 1/(¼) = 4

GMAT Math Review - Arithmetic : Index for Powers & Roots of Numbers

10 more pages in GMAT Math Review