GMAT Exam: A Simple Guide To Arithmetic - Exponents

Terminology
An exponent is a small raised number written to the upper right of a quantity, which is called the base for the exponent.

In the exponential expression bn, b is the base and n is the exponent: .

The act of doing what the exponent indicates is exponentiation.

Types of Exponents
Let m and n be positive integers.

Here are types of exponents and their meanings.

Rules of Exponents
The following rules for exponents hold.


Clarifications About Exponents
 

- An exponent applies only to the base to which it is attached:

(–5)2 = (–5)(–5) = 25, but –52 = –(5·5) = –25

To avoid errors, enclose negative numbers, fractions, and decimals in parentheses.

- Which number is the exponent and which is the base makes a difference in the value of an exponential expression:
25 ≠ 52; 25= 2 × 2 × 2 × 2 × 2 = 32, but 52 = 5 × 5 = 25.

- Exponentiation does not distribute over addition (or subtraction):
(4 + 1)3 ≠ 43 + 13; (4 + 1)3 = (5)3 = 125, but 43 + 13 = 64 + 1 = 65.

- A negative number raised to an even power yields a positive product:
(–3)4 = (–3)(–3)(–3)(–3) = 81.

- A negative number raised to an odd power yields a negative product:
(–3)5 = (–3)(–3)(–3)(–3)(–3) = –243.

- A negative exponent tells you to write a reciprocal; it does not tell you to make your answer negative: