What students learn in AC9M9A01
This unit helps students build a clear, usable understanding of Apply the exponent laws to numerical expressions with integer exponents.... The goal is not to memorise one answer pattern. Students should be able to explain the idea, recognise it in a new example and apply it in a short practice or worksheet task.
- Start with the main idea: apply the exponent laws to numerical expressions with integer exponents and extend to variables.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- representing decimals in exponential form; for example, 0.475 can be represented as 0.475\;=\;\frac4{10}+\frac7{100}+\frac5{1000}\;=\;4\times10^{-1}+7\times10^{-2}+5\times10^{-3} and 0.00023 as 23\times10^{-5} simplifying and evaluating numerical expressions, involving both positive and negative integer exponents, explaining why; for example, 5^{-3}=\frac1{5^3}=(\frac15)^3=\frac1{125} and connecting terms of the sequence 125, 25, 5, 1, \frac15, \frac1{25}, \frac1{125}… to terms of the sequence 5^3, 5^2, 5^1, 5^0,5^{-1},5^{-2},5^{-3}...
- Finish with mixed questions so students must choose the correct strategy rather than copy the last example.
Curriculum coverage and elaborations
The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning but may not appear in the initial eight-question activity.
- Content description: apply the exponent laws to numerical expressions with integer exponents and extend to variables
- E1: representing decimals in exponential form; for example, 0.475 can be represented as 0.475\;=\;\frac4{10}+\frac7{100}+\frac5{1000}\;=\;4\times10^{-1}+7\times10^{-2}+5\times10^{-3} and 0.00023 as 23\times10^{-5}
- E2: simplifying and evaluating numerical expressions, involving both positive and negative integer exponents, explaining why; for example, 5^{-3}=\frac1{5^3}=(\frac15)^3=\frac1{125} and connecting terms of the sequence 125, 25, 5, 1, \frac15, \frac1{25}, \frac1{125}… to terms of the sequence 5^3, 5^2, 5^1, 5^0,5^{-1},5^{-2},5^{-3}...
- E3: relating the computation of numerical expressions involving exponents to the exponent laws and the definition of an exponent; for example, 2^3\div2^5\;=\;2^{-2}\;=\;\frac1{2^2}=\frac14 and (3\times5)^2\;=\;3^2\times5^2\;=\;9\times25\;=\;225
- E4: recognising exponents in algebraic expressions and applying the relevant exponent laws and corresponding conventions; for example, for any non-zero natural number a, a^0\;=\;1, x^1\;=\;x, r^2\;=\;r\times r, h^3\;=\;h\times h\times h, y^4\;=\;y\times y\times y\times y, and \frac1{w} \times \frac1{w}=\frac1{w^2} = w^{-2}
- E5: relating simplification of expressions from first principles and counting to the use of exponent laws; for example, (a^2)^3\;=\;(a\times a)\;\times\;(a\times a)\;\times\;(a\times a)\;=\;a\times a\times a\times a\times a\times a\;=\;a^6; b^2\times b^3\;=\;(b\times b)\times(b\times b\times b)\;=\;b\times b\times b\times b\times b\;=\;b^5; \frac{y^4}{y^2}\;=\;\frac{y\times y\times y\times y}{y\times y}\;=\;\frac{y^2}1\;=\;y^2 and (5a)^2\;=\;(5\times a)\times(5\times a)\;=\;5\times5\times a\times a\;=\;25\times a^2\;=\;25a^2
- E6: applying the exponent laws to simplifying expressions involving products, quotients, and powers of constants and variables; for example, \frac{(2xy)^3}{xy^4}\;=\;\frac{8x^3y^3}{xy^4}\;=\;8x^2y^{-1}
- E7: relating the prefixes for SI units from pico- (trillionth) to tera- (trillion) to the corresponding powers of 10; for example, one pico-gram = 10^{-12} gram and one terabyte = 10^{12} bytes
How to use this unit
Read the topic guide, use the teacher slide for instruction, then complete the Worksheet, Practice and Test. These three activities use the same eight-question unit bank.
Teacher resource
AC9M9A01 teacher slide
Use this one-page PDF to introduce the key idea, vocabulary and teaching sequence before students begin the activities.
Open teacher slide (PDF)Common mistakes to watch for
- Rushing to a rule before checking the concrete model, drawing or number sentence.
- Using the correct answer once but not being able to explain why it works.
- Mixing up similar vocabulary such as more/less, before/after, longer/shorter or equal groups/sharing.
International curriculum mapping
This table gives closest-topic mapping for search and planning. The Australian Curriculum code is exact; overseas entries are broad equivalents because each jurisdiction structures outcomes differently.
| Region | Curriculum | Closest mapping |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M9A01 — apply the exponent laws to numerical expressions with integer exponents and extend to variables |
| Victoria | Victorian Curriculum F-10 | Year 9 Maths: closest match in Algebra. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 5 Maths: closest content focus for Apply the exponent laws to numerical expressions with integer exponents... and related outcomes. |
| United States | Common Core / NGSS | Grade 9 Common Core Mathematics/ELA closest topic match for Apply the exponent laws to numerical expressions with integer exponents.... |
| England / UK | National Curriculum | Key Stage 3 / Year 9: closest programme-of-study match for Apply the exponent laws to numerical expressions with integer exponents.... |
| Canada | Provincial and territory curricula | Grade 9 closest topic match. Canada varies by province, so use this as a broad Ontario/BC-style learning outcome reference. |
| New Zealand | New Zealand Curriculum | Level 5 Maths: closest achievement-objective topic for Apply the exponent laws to numerical expressions with integer exponents.... |
| India | NCERT / CBSE | Class 9 closest NCERT/CBSE topic match for Apply the exponent laws to numerical expressions with integer exponents.... |