AC9M9A01 Year 9 Mathematics

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

Elaborations

• • Elaboration representing decimals in exponential form; for example, 0.475 can be represented as 0.475\;=\;4/10+7/100+5/1000\;=\;4\times10^{-1}+7\times10^{-2}+5\times10^{-3} and 0.00023 as 23\times10^{-5}
• • Elaboration simplifying and evaluating numerical expressions, involving both positive and negative integer exponents, explaining why; for example, 5^{-3}=1/5^3=(1/5)^3=1/125 and connecting terms of the sequence 125, 25, 5, 1, 1/5, 1/25, 1/125… to terms of the sequence 5^3, 5^2, 5^1, 5^0,5^{-1},5^{-2},5^{-3}...
• • Elaboration 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}\;=\;1/2^2=1/4 and (3\times5)^2\;=\;3^2\times5^2\;=\;9\times25\;=\;225
• • Elaboration 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 1/w \times 1/w=1/w^2 = w^{-2}
• • Elaboration 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; y^4/y^2\;=\;y\times y\times y\times y/y\times y\;=\;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
• • Elaboration applying the exponent laws to simplifying expressions involving products, quotients, and powers of constants and variables; for example, (2xy)^3/xy^4\;=\;8x^3y^3/xy^4\;=\;8x^2y^{-1}
• • Elaboration 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