Number Operations · JHS2 Mathematics

Lesson notes

Learning Objectives

Indicator: B8.1.2.3.2 - Apply the laws of indices to simplify and evaluate numbers involving powers of numbers. (PEDMAS)

By the end of the lesson, learners can:

State the laws of indices (product law, quotient law, power of a power law, and zero exponent law) from memory and use them to simplify expressions involving powers of numbers.
Simplify expressions that combine two or more laws of indices, such as 2⁵ × 16².
Evaluate numerical expressions with powers using the order of operations (PEDMAS), giving answers as whole numbers or fractions in simplest form.
Apply the laws of indices to simplify algebraic expressions like y = x^(a-b) × x^(b-c) × x^(c-a) × x^(-a-b).
Solve mixed problems involving negative exponents and fractional powers (such as (81/16)^(-3/4)) and justify each step.

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Curriculum details

Strand: Number (Strand 1)
Sub-strand: Number Operations (1.2)
Content standard: B8.1.2.3 - Demonstrate understanding and the use of the laws of indices in solving problems (including real life problems) involving powers of natural numbers
Indicator: B8.1.2.3.2 - Apply the laws of indices to simplify and evaluate numbers involving powers of numbers. (PEDMAS)
Suggested placement: Term 1, Week 10 (Week 10 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Curriculum reference: Mathematics, Common Core Programme (JHS1-JHS3), 2023, p. 100
Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum)

E.g.1 Use the laws of indices to solve problems involving powers of number.
i) Simplify 2 5 × 16 2
ii) Simplify 27 3 2
iii) Simplify y = x a-b × x b-c × x c-a × x -a-b
iv) Simplify and evaluate ( 16 ) - 3 4 81
v) Evaluate (5 2 ) 3