Outcomes
A student:

 MA5.21WM
selects appropriate notations and conventions to communicate mathematical ideas and solutions

 MA5.23WM
constructs arguments to prove and justify results

 MA5.27NA
applies index laws to operate with algebraic expressions involving integer indices
Content
 Students:
 Apply index laws to algebraic expressions involving integer indices
 use index notation and the index laws to establish that \( a^{1} = \dfrac{1}{a}, \,\, a^{2} = \dfrac{1}{a^2}, \,\, a^{3} = \dfrac{1}{a^3}, \,\, \ldots \)

explain the difference between pairs of algebraic expressions that appear similar,
eg 'Are \( x^{2} \) and \( \!2x \) equivalent expressions? Why or why not?' (Communicating)
 write expressions involving negative indices as expressions involving positive indices, and vice versa

apply the index laws to simplify algebraic products and quotients involving negative indices,
eg \( \, 4b^{5} \times 8b^{3}, \, \) \( 9x^{4} \div 3x^3 \)
 explain why given statements of equality are true or false and give reasons, eg explain why each of the following is true or false: \( \, 5x^0 = 1, \, \) \(9x^5 \div 3x^5 = 3x, \, \) \(a^5 \div a^7 = a^2, \, \) \(2c^{4} = \dfrac{1}{2c^4} \) (Communicating, Reasoning)
 verify whether a given expression represents a correct simplification of another algebraic expression by substituting numbers for pronumerals (Communicating, Reasoning)
 write the numerical value of a given numerical fraction raised to the power of –1, leading to \( \, \left( \! \dfrac{a}{b} \! \right) ^{\!1} = \dfrac{b}{a} \,\) (Communicating, Reasoning)