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Laws of Indices (Same Base, Same Indices)

Learn the laws of indices for multiplying and dividing powers, like am×an=am+na^m \times a^n = a^{m+n} and am÷an=am−na^m \div a^n = a^{m-n}. Let’s get started! 🚀

Laws of Indices (Same Base, Same Indices) - introduction visual

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Laws of indices showing rules for multiplying and dividing powers with same base or same index.Indices example showing 2³ as 2 × 2 × 2, with 2 labelled as base and 3 as index or exponent.Laws of indices chart showing rules for multiplying and dividing powers with the same base, with examples.

🛎️ Indices: Base and Exponent

  • The base is the repeated number and the index (exponent) tells how many times it is multiplied.
  • Example: 23=2×2×22^3 = 2\times2\times2.

🛎️ Laws of Indices: Same Base Rules

  • When you multiply the same base, you add the indices, e.g. 23×24=272^3\times2^4 = 2^7.
  • When you divide the same base, you subtract the indices, e.g. 45÷43=424^5\div4^3 = 4^2.

🛎️ Laws of Indices: Same Index Rules

  • When the index is the same, you multiply the bases, e.g. 23×53=(2×5)3=1032^3\times5^3 = (2\times5)^3 = 10^3.
  • When the index is the same, you divide the bases, e.g. 65÷35=(6÷3)5=256^5\div3^5 = (6\div3)^5 = 2^5.

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