GCSE Maths (AQA)

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Fractional Indices

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Number Structure and Calculation

Fractional Indices

3:50 Advanced Indicies & Roots
Spec N7
Previous Estimating Powers Next Negative Fractional Indices
  • Fractional indices are used to express the power of a root or the root of a power
  • The numerator of the fractional index shows the power that the value is raised to
  • The denominator of the fractional index shows the root of the value
  • The order of raising to the power and taking the root doesn't matter
  • The denominator of the fractional index can be written as a root
  • The identity is: a to the power of x over y is equal to the yth root of a to the x
  • To evaluate 3 to the power of 2 over 5, you can either take the fifth root of 3 squared or take the fifth root of 3 and then square the answer
  • An example is given to evaluate 9 to the power of 3 over 2
  • The easiest form to evaluate is the square root of 9 cubed
  • Evaluating the root and then raising it to the power gives the answer of 27 for 9 to the power of 3 over 2

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