Exponents and Powers
Exponents are useful to express very large numbers, making them shorter and hence easier to understand and compare.
Exponential form is a form involving two numbers written as an , where a is called the base and n is called the exponent.
Expanded form of a number means to expand a number to show the value of each digit.
For a positive integer a, an implies a × a × a × ….n times, i.e. a multiplied by itself n times and an is read as ‘a raised to the power of n’.
Following laws of exponents are obeyed by all numbers in exponential form:
i. 1m = 1
ii. (–1)even number = 1
iii. (–1)odd number = –1
iv. a0 = 1
v. ax × ay = ax+y
vi. ax ÷ ay = ax–y , x > y
vii. (ax )y = ax×y
viii. ay × by = (ab)y
ix. ay ÷ by = (a/b)y
where a and b are non-zero integers and x and y are whole numbers.
A number expressed as a decimal number between 1.0 & 10.0 (including 1.0) multiplied by a power of 10 is said to be in standard form. Standard form is also known as scientific notation.