Key Points - Exponents and Powers

- Exponents: Exponents are used to express large numbers in shorter form to make them easy to read, understand, compare and operate upon.
- Expressing Large Numbers in the Standard Form: Any number can be expressed as a decimal number between 1.0 and 10.0 (including 1.0) multiplied by a power of 10. Such form of a number is called its standard form or scientific motion.
- Very large numbers are difficult to read, understand, compare and operate upon. To make all these easier, we use exponents, converting many of the large numbers in a shorter form.

- The following are exponential forms of some numbers:
10, 000 = 10 ^4 ( read as 10 raised to 4 )

243 = 3^5 ,
128 = 2^7
.
Here, 10, 3 and 2 are the bases, whereas 4, 5 and 7 are their respective exponents. We also say, 10,000 is the 4th power of 10, 243 is the 5th power of 3, etc.

- Numbers in exponential form obey certain laws, which are: For any non-zero integers a and b and whole numbers m and n,

(a) a^m * a^n = a^(m+n)

(b) a^m / a^n = a^(m-n) , m > n
(c) (a^m)^n = a^mn
(d) a^m * b^m = (ab)^m
(e) a^m / b^m = (a/b)^m/n
(f) a0 = 1
(g) (–1) even number = 1 (–1) odd number = – 1