NSW Syllabuses

# Mathematics K–10 - Stage 5.2 - Number and Algebra Indices

## Outcomes

#### A student:

• MA5.2-1WM

selects appropriate notations and conventions to communicate mathematical ideas and solutions

• MA5.2-3WM

constructs arguments to prove and justify results

• MA5.2-7NA

applies index laws to operate with algebraic expressions involving integer indices

## Content

• 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)