Indices

numberandalgebra core

Indices | NSW Curriculum Website

• 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	Prerequisite relationships
Multiplicative Relations A	- Identify prime and composite numbers → Express a number as a product of prime factors
Multiplicative Relations B	- Apply the order of operations → Order of operations with indices
Computation with Integers	- Multiply and divide positive and negative integers → Evaluate numbers in index notation
Fractions Decimals Percentages	- Use approximation notation → Estimate square and cube roots
Algebraic Techniques	- Substitute negative numbers into expressions → Determine the sign of a power

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 (x​) and cube root ($\sqrt[3]{}$)
• 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 $(ab{)}^2=a^2{b}^2$
• Establish the meaning of the zero index
• Apply index laws to simplify and evaluate expressions with numerical bases