Summary: Exponents & Powers

Exponents

• Exponents are used to express large numbers in shorter form to make them easy to read, understand, compare and operate upon. For example, 10, 000 = 10 × 10 × 10 × 10 = 10⁴.

Laws of Exponents

1. Multiplying Powers with the Same Base

• For any non-zero integer a and whole number m and n, a^m × aⁿ = a^m+n

2. Dividing Powers with the Same Base

• For any non-zero integer a and whole number m and n (m>n), a^m ÷ aⁿ = a^m-n

3. Taking Power of a Power

• For any non-zero integer a and whole number m and n, (a^m)ⁿ = a^mn

4. Multiplying Powers with the Same Exponents

• For any non-zero integers a and b and whole number m, a^m × b^m = (ab)^m

5. Dividing Powers with the Same Exponents

• For any non-zero integers a and b and whole number m, a^m ÷ b^m = a^m/b^m = (a/b)^m

Expressing large numbers in the standard form

• 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 a form of a number is called its standard form or scientific notation. For example: Speed of light in vacuum = 300000000 m/s = 3.0 × 10⁸ m/s.