2.1 Laws of indices

AQA Edexcel OCR A OCR B (MEI)
Understand and use the laws of indices for all rational exponents.

"Index" (plural: "indices") and "exponent" mean the same thing as "power".
Important
The laws of indices:

  • \(a^x×a^y=a^{x+y}\)
  • \(a^x÷a^y=a^{x-y}\)
  • \((a^x)^y=a^{xy}\)
  • \((ab)^y=a^xb^x\)

Fractional and negative powers:

  • \(a^{\frac{1}{y}}=\sqrt[y]{a}\)
  • \(a^{\frac{x}{y}}=\sqrt[y]{a^x}\)
  • \(a^{-x}=\dfrac{1}{a^x}\)

Also remember:

  • \(a^0=1\)
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