Laws of Indices
What are the laws of indices?
- There are lots of very important laws (or rules)
- It is important that you know and can apply these
- Understanding the explanations will help you remember them
Law | Description | Why |
anything to the power 1 is itself | ||
to multiply indices with the same base, add their powers | ||
to divide indices with the same base, subtract their powers | ||
to raise indices to a new power, multiply their powers | ||
anything to the power 0 is 1 | ||
a negative power is "1 over" the positive power | ||
a power of an nth is an nth root | ||
a fractional power of m over n means either - do the the nth root first, then raise it to the power m or - raise it to the power m, then take the nth root (depending on what's easier) |
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a power outside a fraction applies to both the numerator and the denominator | ||
flipping the fraction inside changes a negative power into a positive power |
Changing the base of a term
- Sometimes expressions involve different base values
- You can use index laws to change the base of a term to simplify an expression involving terms with different bases
- For example
- Using the above can then help with problems like
Exam Tip
- Index laws only work with terms that have the same base, so something like 23 × 52 cannot be simplified using index laws