Exponents and Powers | SOF Olympiad Trainer

EXPONENTS AND POWERS- ESSENTIAL POINTS

Numbers with negative exponents follow these laws:
1. a^mx aⁿ = a^m+n
2. a^m aⁿ = a^m-n , m > n
3. (a^m)ⁿ = a^mn
4. a^m x b^m = (ab)^m
5. a^m b^m = (a/b)^m
6. a⁰ = 1
Very small numbers can be expressed in standard form using negative exponents.
Use of Exponents to Express Small Number in Standard form:
1. Very large and very small numbers can be expressed in standard form.
2. Standard form is also called scientific notation form.
3. A number written as m x 10ⁿ is said to be in standard form if m is a decimal number such that 1≤ m < 10 and n is either a positive or a negative integer. Examples: 150,000,000,000 = 1.5 x 10¹¹.
Exponential notation is a powerful way to express repeated multiplication of the same number. For any non-zero rational number ‘a’ and a natural number n, the product a x a x a …. x a (n times) = aⁿ. It is known as the nth power of ‘a’ and is read as ‘a’ raised to the power n. The rational number a is called the base and n is called exponent.