Reach for the Star

Powers roots and index laws · Optional extension

L053 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

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

Reveal a worked check after attempting

6x⁶y⁴; multiplication needs no non-zero assumption.

Deep challenge

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

Reveal a worked check after attempting

No; index laws apply to products, not sums. At x=2, 32+8=40, not 256.

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.