#NumberAndAlgebra #Core >[!info]- [Indices | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/content/stage-4/fa5d58f980) >- MA4-INT-C-01 operates with primes and roots, positive-integer and zero indices involving numerical bases and establishes the relevant index laws ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | ---------------------------------- | ---------------------------- | ------------------------------------------ | | [[Multiplicative Relations A]] | - factors and primes | - prime factorisation | | [[Multiplicative Relations B]] | - order of operations | - evaluating expressions involving indices | | [[Computation with Integers]] | - operations with integers | - simplifying using index laws | | [[Fractions Decimals Percentages]] | - simplifying fractions | - establishing the index laws | | [[Algebraic Techniques]] | - generalising relationships | - establishing the index laws | ## [[Apply index notation to represent whole numbers as products of powers of prime numbers.pdf]] - Describe numbers written in index form using terms such as _base_, _power_, _index_ and _exponent_ - Represent numbers in index notation limited to positive powers - Represent in expanded form and evaluate numbers expressed in index notation, including powers of 10 - Apply the order of operations to evaluate expressions involving indices - Determine and apply tests for divisibility for 2, 3, 4, 5, 6 and 10 - Represent a whole number greater than one as a product of its prime factors, using index notation where appropriate ## [[Examine cube roots and square roots.pdf]] - Use the notations for square root ($\sqrt{\phantom{x}}$) and cube root ($\sqrt[3]{\phantom{x}}$) - Recognise and describe the relationship between squares and square roots, and cubes and cube roots for positive numbers - Verify, through numerical examples, that $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ - Estimate the square root of any non-square whole number and the cube root of any non-cube whole number, then check using a calculator - Identify and describe exact and approximate solutions in the context of square roots and cube roots - Apply the order of operations to evaluate expressions involving square roots, cube roots, square numbers and cube numbers ## [[Use index notation to establish the index laws with positive-integer indices and the zero index.pdf]] - Establish the multiplication, division and the power of a power index laws, by expressing each number in expanded form with numerical bases and positive-integer indices - Verify through numerical examples that $(ab)^2=a^2b^2$ - Establish the meaning of the zero index - Apply index laws to simplify and evaluate expressions with numerical bases