AC9M8N02 Year 8 Mathematics

This Content Descriptor from Year 8 Mathematics provides the specific knowledge and skills students should learn. Use it to plan lessons, create learning sequences, and design assessments that align with the Australian Curriculum v9.

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

Elaborations

• 1 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
• 2 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, \(\frac{6^3}{2^3}\;=\;\frac{2^3\times3^3}{2^3}\;=\;3^3\), so the volume is increased by a factor of \(27\)
• 3 using digital tools to systematically explore the application of the exponent laws; observing that the bases need to be the same
• 4 using examples such as \(\frac{3^4}{3^4}\;=\;1\), and \(3^{4-4}\;=\;3^0\) to illustrate the necessity that for any non-zero natural number \(n,\;n^0\;=\;1\)

Related Achievement Standards