A worksheet on powers of rational numbers. The exercises require to evaluate, compare and order powers in which the base is a positive or negative integer or fraction. Solutions are included.

Looking for a no-prep, comprehensive practice worksheet to help your pupils master indices with negative bases and fractional bases?

This robust practice resource is specifically designed to build conceptual understanding and procedural fluency with powers. It moves students through a beautifully scaffolded progression—starting with basic evaluation, advancing to comparing and ordering exponential expressions, and culminating in advanced mathematical puzzles involving repeating series of positive and negative ones.

Perfect for Key Stage 3 (KS3) core curriculum mastery, advanced Key Stage 2 (KS2) extension, or as an intensive GCSE foundation and higher maths revision packet at the start of the term!

What’s Included:

• Pages 1–2 (4 Comprehensive Question Sets): A clean, beautifully organized layout featuring large, clear question boxes that give pupils plenty of space to write.
  Section 1 (Evaluate): 24 questions evaluating powers with integer bases, negative bases, zero indices, and fractional bases.
  Section 2 (Compare): 10 challenging questions asking pupils to use inequalities to compare large indices expressions without calculating them fully (testing even/odd power rules with negative bases).
  Section 3 (Order): 2 multi-part tasks requiring pupils to sort expressions into ascending order.
  Section 4 (Advanced Series): 4 high-level expressions asking pupils to evaluate long, repeating addition chains of 1 and -1 raised to various powers.
• Full Step-by-Step Answer Key: Pages 3–4 contain a complete, beautifully clear solutions guide showing the final values and simplified relationships for all tasks. This makes marking incredibly fast or allows for flawless pupil self-checking!

How to Use This in Your Classroom:

• Independent Classwork or Multi-Lesson Homework / Prep Assignment Packet
• End-of-Unit Revision, Exam Prep, or Low-Stakes Assessment
• Maths Mastery Workshops, Choice Boards, or Rotation Stations
• Emergency Cover Plans (the detailed answer key handles the teaching for you!)
• Small Group Intervention and Maths Remediation

Educational Standards & Curriculum Alignment:
UK National Curriculum (Key Stage 3 & 4 Mathematics):

• Number: Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5. Order positive and negative integers, decimals and fractions.
• Understand the behavior of negative numbers when raised to odd or even powers.