Powers and Indices

Learn how powers work, including bases and exponents. Let’s get started! 🚀

Powers and Indices - introduction visual

Video Lesson

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Flashcards

Review key concepts visually

Introduction to powers by showing the relationship that 3+3+3+3 equals 4 times 3, and 3 x 3 x 3 x 3 equals 3 to the power of 4.Explanation of the base 3 and index 4 in 3^4 that it is pronounced 'three to the power of four'.Explaining key characteristics of powers, e.g., 3^4 is not the same as 4^3, a^1 is a, and for a different to 0, a^0 is 1.Common indices chart showing square and cube numbers with examples. For example, square numbers 1, 4, 9, 16, and cube numbers 1, 8, 27, 64, 125.Cartoon blue bird explaining how to simplify 4 × 3 × 3 × 4 × 4 to 4³ × 3² using commutative and associative laws.BIDMAS calculation rules with indices shown by comparing (2 × 5)^2 and 2 × 5^2, resulting in 100 and 50 respectively.

🛎️ What are Powers?

  • Powers show repeated multiplication of the same number.
  • For example, 3⁴ means 3 × 3 × 3 × 3.

🛎️ How to Read Powers

  • The base is the number being multiplied.
  • The power (small number at the top right) shows how many times it is multiplied.

🛎️ Important Properties of Powers

  • Any number to the power of 1 equals itself (e.g. 5¹ = 5).
  • Any number (except 0) to the power of 0 equals 1 (e.g. 5⁰ = 1).

🛎️ Common Powers: Squares and Cubes

  • Square numbers have power 2 (e.g. 4² = 16).
  • Cube numbers have power 3 (e.g. 3³ = 27).

🛎️ Simplifying Expressions with Powers

  • First, group the same numbers together in multiplication.
  • Then, write repeated multiplication using **powers. **

🛎️ Calculating with Powers

  • Following BIDMAS, work out **powers before multiplication. **
  • But if there are brackets, calculate inside the brackets first.

Practice Questions

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Interactive Activity

Practice grouping factors to create exponent expressions

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