# Exponentiation is not commutative.For example, 2 3 = 8 ≠ 3 2 = 9. Exponentiation is not associative.For example, (2 3) 4 = 8 4 = 4096, whereas 2 (3 4) = 2 81 = 2 417 851 639 229 258 349 412 352.

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For example: in 5 3, 5 is the "base" and 3 is the "index". The plural of "index" is "indices". Indices show repeated multiplication, eg. 5 3 = 5 x 5 x 5. All of the other index laws are based on the simple facts above. The page below will explain why.

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## There are 6 Index laws which needs to be remembered. Step 2: Use the second law of indices: 43 Step 4: We cancel the “4” and are left with the following:.

We read this as ‘three to the power We know that: In general: This formula tells us that when a product is raised to a power, every factor of the product is raised to the power. This is the fifth index law and is known as the Index Law for Powers of Products.. Example 12.

### Index Law 4 - The power of a product can be written as the product of the powers.

Clearly the index laws need to be integrated into algebra. This module does not involve anything but very simple fractions, so it deals only with the three index laws involving products. The remaining two index laws are left until the next 2020-07-26 · Learn about and revise how to multiply and divide indices, as well as apply negative and fractional rules of indices with GCSE Bitesize AQA Maths.

12 y = 4. 3 b = 3. 8 x = 2. 13 y = 5/3. 4 m = 3. 9 x = 0.8. 14 d = -2.

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Index Laws• How can I simplify 95 ÷ 93?

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### Part 4 – Index laws: Raising a power to a power. Click slide to play video. Click slide to play video. Teacher resources for Part 4. Teachers: log in to access the

√ am = a m n . Zero power. Index laws.