Class 8 Chapter 2: Powers and Exponents

# Class 8 Chapter 2: Powers and Exponents

Important Concepts and Formulas on Exponents

1.      The exponential form of a given number is a way of expressing it using a base and a raised number called exponent. For example, in 52, the base is 5 and the exponent is 2.

2.      128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 is product form of 128 with base 2.

3.      When base is positive, the result will be positive.

4.      When base is negative and power is an odd number, the result will be negative.

5.      When base is negative and power is an even number, the result will be positive.

6.      When 1 is raised to any power, the result will be equal to 1.

7.      We denote the reciprocal of a number a by a–1, i.e. a–1 = 1/a . Hence, the reciprocal of (p/q)m is (q/p)m.

8.      The following are the laws of exponents for a and b which are non-zero integers and m and n are whole numbers.

·        am × an = am + n
·        am ÷ an = am – n , when m > n
·        (am)n = amn
·        am × bm = (ab)m
·        am ÷ bm = (a/b)m
·        a0 = 1

9.      (–1)even number = 1 and (–1)odd number = –1

10. Standard form is a way of writing very large numbers or very small numbers in short form.

11. The standard form of a number is a × 10b, where 1 ≤ a < 10 and b is an integer. For example, 61,20,000 can be written as 6.12 × 106.