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