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C1 Topic 2: Algebra
The laws of indices backmore
When we write something like 4^7, the 7 is called the "power" or "exponent" or "index", and we can read it as "4 to the power 7".
So 4^7 means 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4.
Remember that:
a^1 = a
a^2 = a \times a
a^3 = a \times a \times a
a^4 = a \times a \times a \times a
and so on...
... and a^0 = 1
Note also that 3x to the power 4 means
(3x)^4 = 3x \times 3x \times 3x \times 3x = 3^4x^4 = 81x^4
There are three basic rules of indices that you should have met before in GCSE Mathematics. Can you see what they are?



Summary
The three rules of indices are:
  • a^m \times a^n = a^{m+n}
  • a^m \div a^n = a^{m-n}
  • (a^m)^n = a^{mn}
Make sure you know and understand these three rules. They will turn up again and again throughout your course. Remember also that
  • \displaystyle a^{-n} = \frac{1}{a^n}
  • a^0 = 1
  • a^{\frac{1}{n}} =\displaystyle \root n \of{a}
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