Laws of indices
Rules for combining powers. Add the powers when multiplying, subtract when dividing, and multiply them for a power of a power.
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Analogy
Like stacking blocks: 2^3 is three twos, 2^4 is four twos, so together you have seven twos.
Example
2^3 x 2^4 = 2^7 = 1285^6 / 5^4 = 5^2 = 25(3^2)^3 = 3^6 = 729
In practice
Computer memory sizes such as 2^10 = 1,024 rely on these rules.
Practice
Flashcards
- What is 2^3 x 2^4 as a single power?2^7. When multiplying powers of the same base, add the indices.
Questions people ask
What does a negative power mean?
A negative power means 'one over' the positive power. So 2^-3 = 1/2^3 = 1/8. It does not make the answer negative. It flips the number to the bottom of a fraction. A power of zero is always 1. For example, 10^-2 is 1/100, which is 0.01. Negative powers are how very small numbers are written.
Why is any number to the power 0 equal to 1?
Use the division rule. 5^3 / 5^3 = 5^0, but any number divided by itself is 1. So 5^0 = 1. The same logic works for every number except zero, which gives no sensible answer. For example, 10^3 / 10^3 = 1000 / 1000 = 1, which is also 10^0. The rule keeps all the index laws working together.