Lesson

1.1 EXPONENTIAL




After completing this section, you should be able to:

  • write normal numerals using index notation: \( 8 = 2^3 \)
  • simplify algebraic expressions by multiplication using exponents: \( 2^3 \times 2^6 = 2^9 \)
  • simplify algebraic expressions by division using exponents: \( 2^9 \div 2^6 = 2^3 \)
  • simplify algebraic expressions by zero index: \( 2^0 = 1 \)
  • simplify algebraic expressions by raising a power to another power” \( (2^3)^4 = 2^12 \)
  • simplify algebraic expressions by negative exponents: \( \displaystyle 2^{-3} = \dfrac{1}{2^3} \)
  • simplify algebraic expressions by rational exponents: \( 2^{\frac{3}{4}} = \sqrt[4]{2^3} \)
  • simplify complicated algebraic expressions by exponent laws
  • simplify algebraic expansion with exponents: \( 2^3(2^2 + 2^5) = 2^5 + 2^8 \)
  • simplify algebraic expressions by algebraic factorisation with exponents: \( 2^8 + 2^3 = 2^3(2^5 + 1) \)
  • solve exponential equations: \( 2^x = 8 \)
  • sketch exponential graphs
  • calculate the value of natural exponential: \( e^3 \approx 20.08 \cdots \)
  • sketch natural exponential graphs
  • solve practical applications of exponential growth
  • solve practical applications of exponential decay