Mixed laws of indices practice

2026-11-29Algebraic Manipulation Mr Ng

Combine product, quotient and power laws in one simplification.

Key formulas

(a^m)^n = a^{mn}

a^m/a^n = a^{m−n}

What this lesson covers

This lesson builds Secondary 2–3 skill in mixed indices. Read the key formulas, study the worked example, then attempt the written practice and the four-question MCQ review.

Method

Write every step. Name the rule you use (mixed indices) before substituting numbers. Keep units and signs visible until the final sentence.

Common mistakes

Students often rush the sign, use the wrong percentage base, or cancel terms instead of factors. Pause after each line and ask whether the step is reversible.

Exam habit

Underline the question verb (simplify, solve, factorise, find). Box the final answer and, where sensible, substitute back for a quick check.

Worked example

Worked example — mixed indices

Problem. Apply the method for mixed indices with the numbers 7 and 6.

Solution. Identify the rule for mixed indices. Substitute 7 and 6 carefully with signs in brackets if needed. Complete each operation on a new line. State the final answer clearly and check by reversing one step.

Review quiz

1 / 4

Warm-up on mixed indices: what is 9+4?

Practice questions

Practice 1 on mixed indices: compute with the value 37.
Practice 2 on mixed indices: change the numbers and repeat the same method.
Practice 3 on mixed indices: write one sentence explaining the key rule.
Practice 4 on mixed indices: invent a similar exam-style question and solve it.

Study notes

What is the main idea of mixed indices?

Apply the stated formula or rule with clear steps, then check by reversing or substituting.

How should I revise this topic?

Cover the worked example, redo the practice without notes, then complete the MCQ set and log any wrong options.