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Count factors before using the shortcut - Paper 1

Read the information, then answer the questions. An adult may read the instructions aloud. Show your working where asked.

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Use non-zero base a. In this notation ^ means 'to the power of'. Multiplying same-base powers combines repeated factors; dividing cancels factors. Compare a^6 x a^2, a^8 / a^6, and the DIFFERENT operation a^6 + a^2. Addition does not use the multiplication index law.

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  1. Simplify a^6 x a^2 and explain using repeated factors.
  2. Simplify a^8 / a^6. Why require a to be non-zero?
  3. Test the false claim a^6 + a^2 = a^8 using a = 2.

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