EXPONENTS AND POWERS- ESSENTIAL POINTS
- Exponents are used to express large numbers in shorter form to make them easy to read, understand, compare and operate upon.
- 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 notion.
- 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. For example
- 100000 = 105 (read as 10 raised to 5)
- 512 = 29
- 243 = 35
- Here, 10, 3 and 2 are the bases, whereas 5, 5 and 9 are their respective exponents. We also say, 1,00,000 is the 5th power of 10, 243 is the 5th power of 3, etc.
- If a and b are integers and m, n are any whole numbers, then
- am x an = am+n
- am an = am-n , m > n
- (am)n = amn
- am x bm = (ab)m
- am bm = (a/b)m
- a0 = 1
