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Writing indices and index laws

Writing indices and index laws

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Summary

Writing indices and index laws

​​In a nutshell

Indices are used as shorthand for repeated multiplication. Another term for indices is "powers".



Writing indices

Indices are written as a small number to the top right of another number. The index number (also called the power) tells you the number of times you multiply the bigger number by itself.


Examples
  • 545^4​ is shorthand for 5×5×5×5=6255\times5\times5\times5=625. It is read as "five to the power of four".
  • 15215^2is shorthand for 15×15=22515\times15=225. Anything to the power of two is called "squared". In this case, this is read as "fifteen squared".
  • 131^3is shorthand for 1×1×1=11\times1\times1=1. Anything to the power of three is called "cubed". In this case, this is read as "one cubed".



Index laws

Index laws (or the laws of indices) are a set of rules that help with writing powers or multiplying/dividing with them. Here are the rules:


The six index laws

  1. When multiplying two powers of the same number, add the powers.
  2. When dividing two powers of the same number, subtract the powers.
  3. When raising a power to another power, multiply the powers.
  4. A negative power is the same as turning the number "upside down" like a fraction.
  5. ​Anything to the power of 11 is itself.
  6. Anything to the power of 00 is 11.​


Examples
  1. 63×65=63+5=686^3\times6^5=6^{3+5}=6^8​​
  2. 137÷132=137(2)=13913^7\div13^{-2}=13^{7-(-2)}=13^9​​
  3. (28)3=28×3=224(2^8)^3=2^{8\times3}=2^{24}​​
  4. 35=1353^{-5}=\frac{1}{3^5}​​
  5. 331=3333^1=33​​
  6. 330=133^0=1​​


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FAQs - Frequently Asked Questions

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