Exponents and Powers

• Introduction to Exponents
  • Meaning of Base and Exponent (Index/Power)
  • Example: $2^5$ (2 is base, 5 is exponent)
  • Reading: "2 raised to the power 5"
  • Meaning: $2 \times 2 \times 2 \times 2 \times 2 = 32$
  • Expressing large numbers using exponents
• Laws of Exponents
  • Multiplying powers with the same base: $a^m \times a^n = a^{m+n}$
  • Dividing powers with the same base: $a^m \div a^n = a^{m-n}$
  • Taking power of a power: $(a^m)^n = a^{m \times n}$
  • Multiplying powers with the same exponents: $a^m \times b^m = (ab)^m$
  • Dividing powers with the same exponents: $a^m \div b^m = (a/b)^m$
  • Number with exponent zero: $a^0 = 1$ (where $a \neq 0$)
• Decimal Number System
  • Expanding numbers using powers of 10
  • Example: $47561 = 4 \times 10^4 + 7 \times 10^3 + 5 \times 10^2 + 6 \times 10^1 + 1 \times 10^0$
• Expressing Large Numbers in Standard Form
  • Also known as Scientific Notation
  • Form: $k \times 10^n$ (where $1 \le k < 10$ and $n$ is an integer)
  • Example: $5985.3 = 5.9853 \times 10^3$
  • Example: $5,00,00,000 = 5 \times 10^7$