Exponents and Powers

• Introduction to Exponents
  • Meaning of Base and Exponent
  • Reading and writing numbers in exponential form ($a^n$)
  • Example: $2^3 = 2 \times 2 \times 2 = 8$
• Laws of Exponents
  • Multiplying Powers with the Same Base: $a^m \times a^n = a^{m+n}$
  • Dividing Powers with the Same Base: $a^m \div a^n = a^{m-n}$
  • Power of a Power: $(a^m)^n = a^{m \times n}$
  • Multiplying Powers with the Same Exponents: $a^m \times b^m = (a \times b)^m$
  • Dividing Powers with the Same Exponents: $a^m \div b^m = (a/b)^m$
  • Number with Exponent Zero: $a^0 = 1$ (where $a \neq 0$)
• Negative Exponents
  • Definition: $a^{-m} = \frac{1}{a^m}$
  • Multiplicative inverse of $a^m$ is $a^{-m}$
  • Handling negative exponents in numerators and denominators
• Use of Exponents to Express Small Numbers in Standard Form
  • Concept of Standard Form (Scientific Notation)
  • Format: $k \times 10^n$ (where $1 \le k < 10$ and $n$ is an integer)
  • Converting very large numbers to standard form
  • Converting very small numbers to standard form using negative powers of 10
  • Comparison of very large and very small numbers