AC9M9A01

Elaborations

• AC9M9A01_E1representing decimals in exponential form; for example, 0.475 can be represented as 0.475 = 4/10+7/100+5/1000 = 4×10^-1+7×10^-2+5×10^-3 and 0.00023 as 23×10^-5
• AC9M9A01_E2simplifying 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...
• AC9M9A01_E3relating the computation of numerical expressions involving exponents to the exponent laws and the definition of an exponent; for example, 2^3÷2^5 = 2^-2 = 1/2^2=1/4 and (3×5)^2 = 3^2×5^2 = 9×25 = 225
• AC9M9A01_E4recognising 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×r, h^3 = h×h×h, y^4 = y×y×y×y, and 1/w ×1/w=1/w^2 = w^-2
• AC9M9A01_E5relating simplification of expressions from first principles and counting to the use of exponent laws; for example, (a^2)^3 = (a×a) × (a×a) × (a×a) = a×a×a×a×a×a = a^6; b^2×b^3 = (b×b)×(b×b×b) = b×b×b×b×b = b^5; y^4/y^2 = y×y×y×y/y×y = y^2/1 = y^2 and (5a)^2 = (5×a)×(5×a) = 5×5×a×a = 25×a^2 = 25a^2
• AC9M9A01_E6applying 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
• AC9M9A01_E7relating 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