Class 7 Chapter 5: Powers and Exponents

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

      ·        a^m × aⁿ = a^{m + n}

      ·        a^m ÷ aⁿ = a^{m – n} , when m > n

      ·        (a^m)ⁿ = a^mn

      ·        a^m × b^m = (ab)^m

      ·        a^m ÷ b^m = (a/b)^m

      ·        a⁰ = 1

4.      (–1)^{even number} = 1 and (–1)^{odd number} = –1

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

6.      The standard form of a number is a × 10^b, where 1 ≤ a < 10 and b is an integer.