RevTree
Back to skills
#235

Estimating roots and powers

Number · Grade 4–6

Strand: Number Substrand: Roots and powers Sparx code: U299 Sparx levels: 3, 4, 5 Tier: Higher Only

Key steps (method)

  • Write everything in index form where possible.
  • Use index laws: multiply → add powers, divide → subtract powers, power of a power → multiply powers.
  • Handle negative and zero indices: a^0 = 1, a^ = 1/a^n.
  • Simplify coefficients and collect like terms carefully.
  • Check by substituting an easy number (e.g. a = 2) if you’re unsure.

Common mistakes

  • Adding powers when you should subtract (or vice versa).
  • Forgetting that a^0 = 1 (for a ≠ 0).
  • Leaving negative indices when the question expects positive powers.
  • Applying index laws to sums (e.g. (a+b)^2 ≠ a^2+b^2).

Quick notes

  • If you get stuck, try a simpler version of the problem first or plug in easy numbers to test your method.
  • For multi-step questions, label each step and keep intermediate results.
  • For exam questions, always aim to make your work “mark-scheme readable”.

Self-assessment

  • Can I define it? Write a one-sentence definition of Estimating roots and powers (or the key term in the question).
  • Can I do it? Do 3 questions: one easy, one standard, one harder. Don’t look at notes until you’ve tried.
  • Can I explain it? In 2–3 sentences, explain why the method works (or what would go wrong with a common mistake).
  • Can I check it? State one quick check (estimate, units, sign, reasonableness).

Support videos

Notes