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4 - Mathematics M1.AL.4 - Laws of Indices

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  • ✓use the laws of indices to manipulate expressions with integral indices: xᵐ × xⁿ = xᵐ⁺ⁿ
  • ✓xᵐ ÷ xⁿ = xᵐ⁻ⁿ
  • ✓(xᵐ)ⁿ = xᵐⁿ
  • ✓x⁻ᵐ = 1/xᵐ
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A microbiologist at the UWI lab counts 1 bacterium at 8 a.m. By 9 a.m. there are 2 (one doubling), by 10 a.m. 4, by 11 a.m. 8, by noon 16. After n hours: 2ⁿ. That power notation rules biology, finance, computing, and all of CSEC algebra.
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Memory Hook / Mnemonic: MAD. Multiply Add (powers); Divide Subtract; Power-of-power Multiply.
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Make a prediction before we start: Which statement do you think best describes index / exponent?

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A microbiologist at the UWI lab counts 1 bacterium at 8 a.m. By 9 a.m. there are 2 (one doubling), by 10 a.m. 4, by 11 a.m. 8, by noon 16. After n hours: 2ⁿ. That power notation rules biology, finance, computing, and all of CSEC algebra.
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