AC9M9A01

See also: Learning Areas / Mathematics / Mathematics / Algebra / Year 9

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

Elaborations
  • AC9M9A01_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 \(23\times10^{-5}\)
  • AC9M9A01_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 \(5^3\), \(5^2\), \(5^1\), \(5^0\),\(5^{-1}\),\(5^{-2}\),\(5^{-3}\)...
  • AC9M9A01_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 \((3\times5)^2\;=\;3^2\times5^2\;=\;9\times25\;=\;225\)
  • AC9M9A01_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 \(\frac1{w} \times \frac1{w}=\frac1{w^2} = w^{-2}\)
  • AC9M9A01_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 \((5a)^2\;=\;(5\times a)\times(5\times a)\;=\;5\times5\times a\times a\;=\;25\times a^2\;=\;25a^2\)
  • AC9M9A01_E6 - applying the exponent laws to simplifying expressions involving products, quotients, and powers of constants and variables; for example, \(\frac{(2xy)^3}{xy^4}\;=\;\frac{8x^3y^3}{xy^4}\;=\;8x^2y^{-1}\)
  • AC9M9A01_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
Achievement Standard Components
  • ASMAT902 - They extend and apply the exponent laws with positive integers to variables.