Reach for the Star | GCSE Mathematics

L053: Powers roots and index laws

Objective

Use powers, roots and index laws with valid conditions.

Calculator: Non-calculator core; calculator optional only for checking where labelled.

Visual model for Powers roots and index laws
Points route: Connect 2 · Share 2 · Apply 6 · Review 3 · Stretch 2 · Deep Challenge 3. Record your score honestly after you have checked your answer.

Recall

Retrieve the key fact or method needed for powers roots and index laws.

Core practice

Simplify (3x²y³)(2x⁴y) and state any assumptions.

Reasoning

Is x⁵+x³=x⁸? Show why or give a counterexample.

Exam-style

Solve an exam-style problem involving powers roots and index laws. Show working, include a check and interpret your answer.

WWW / EBI

Recall & Review: feedback and extension integration

Lesson L053: Powers roots and index laws

Objective: Use powers, roots and index laws with valid conditions.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I selected an efficient numerical method, showed the key steps clearly and checked the sign, size or accuracy of my answer.

Even Better If (EBI)

I will make the place-value, sign or operation decision explicit and use estimation or an inverse calculation to check a fresh question.

Stretch and deep challenge

Stretch: Simplify (3x²y³)(2x⁴y) and state any assumptions.

Deep challenge: Is x⁵+x³=x⁸? Show why or give a counterexample.