AC9M8N02

Elaborations

• AC9M8N02_E1recognising the connection between exponent form and expanded form with the exponent laws of product of powers rule, quotient of powers rule, and power of a power rule; for example, 2^3×2^2 can be represented as (2×2×2)×(2×2)=2^5 and connecting the result to the addition of exponents
• AC9M8N02_E2applying the exponent laws of the product of powers rule, quotient of powers rule, power of a power rule and zero exponent individually and in combination; for example, using exponents to determine the effect on the volume of a 2 centimetre cube when the cube is enlarged to a 6 centimetre cube, 6^3/2^3 = 2^3×3^3/2^3 = 3^3, so the volume is increased by a factor of 27
• AC9M8N02_E3using digital tools to systematically explore the application of the exponent laws; observing that the bases need to be the same
• AC9M8N02_E4using examples such as 3^4/3^4 = 1, and 3^4-4 = 3^0 to illustrate the necessity that for any non-zero natural number n, n^0 = 1