AC9M9A01 Year 9 Mathematics

This Content Descriptor from Year 9 Mathematics provides the specific knowledge and skills students should learn. Use it to plan lessons, create learning sequences, and design assessments that align with the Australian Curriculum v9.

apply the exponent laws to numerical expressions with integer exponents and extend to variables

Elaborations

• 1 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 \(23\times10^{-5}\)
• 2 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 \(5^3\), \(5^2\), \(5^1\), \(5^0\),\(5^{-1}\),\(5^{-2}\),\(5^{-3}\)...
• 3 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 \((3\times5)^2\;=\;3^2\times5^2\;=\;9\times25\;=\;225\)
• 4 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 \(\frac1{w} \times \frac1{w}=\frac1{w^2} = w^{-2}\)
• 5 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 \((5a)^2\;=\;(5\times a)\times(5\times a)\;=\;5\times5\times a\times a\;=\;25\times a^2\;=\;25a^2\)
• 6 applying the exponent laws to simplifying expressions involving products, quotients, and powers of constants and variables; for example, \(\frac{(2xy)^3}{xy^4}\;=\;\frac{8x^3y^3}{xy^4}\;=\;8x^2y^{-1}\)
• 7 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

Related Achievement Standards