AC9M8N02 Year 8 Mathematics

Content descriptor establish and apply the exponent laws with positive integer exponents and the zero-exponent, using exponent notation with numbers

Elaborations

• • Elaboration recognising 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\times2^2 can be represented as (2\times2\times2)\times(2\times2)=2^5 and connecting the result to the addition of exponents
• • Elaboration applying 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\times3^3/2^3\;=\;3^3, so the volume is increased by a factor of 27
• • Elaboration using digital tools to systematically explore the application of the exponent laws; observing that the bases need to be the same
• • Elaboration using 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