# Powers And Roots Worksheet • Section 1 of the powers and roots worksheet contains 36 skills-based powers and roots questions, in 3 groups to support differentiation
• Section 2 contains 4 applied powers and roots questions with a mix of worded problems and deeper problem solving questions
• Section 3 contains 4 foundation and higher level GCSE exam style powers and roots  questions
• Answers and a mark scheme for all powers and roots questions are provided
• Questions follow variation theory with plenty of opportunities for students to work independently at their own level
• All questions created by fully qualified expert secondary maths teachers
• Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards

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### Powers and roots at a glance

Powers, or exponents, are numbers written in superscript and denote repeated multiplication. The simplest case is square numbers where a superscript 2, this shows that a number is multiplied by itself. For cube numbers, with a superscript 3, the multiplication is carried out three times and so on for any integer (whole number) power.

Rooting is the inverse operation. The square root is the inverse of squaring, the cube root is the inverse of cubing, and so on. The root finds the original number that was multiplied.

The laws of indices extend these ideas to explain what happens when we multiply, divide or carry out other operations on expressions containing powers, both numeric and algebraic. We can extend these ideas further to using negative numbers or fractions as powers, and estimating powers and roots using known facts.

Looking forward, students can then progress to additional number worksheets, for example a or a For more teaching and learning support on Number our GCSE maths lessons provide step by step support for all GCSE maths concepts.

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