AC9M8N02

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

Elaborations

AC9M8N02_E1 - 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
AC9M8N02_E2 - 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 \(27\)
AC9M8N02_E3 - using digital tools to systematically explore the application of the exponent laws; observing that the bases need to be the same
AC9M8N02_E4 - 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 \(n,\;n^0\;=\;1\)

Achievement Standard Components

ASMAT802 - They apply the exponent laws to calculations with numbers involving positive integer exponents.