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Exponent Rules
What are Exponents?
Exponents are used to show repeated multiplication of a number by itself. For example, $7 * 7 * 7$ can be represented as $7^3$.
Here are some other examples:
- $3^4 = 3 * 3 * 3$
- $10^5 = 10 * 10 * 10 * 10 * 10$
- $16^2 = 16*16$
Suppose, a number ‘a’ is multiplied by itself n-times, then it is represented as an where a is the base and n is the exponent.
Exponents follow certain rules that help in simplifying expressions which are also called its laws. Let us discuss the laws of exponents in detail.
Rules of Exponents With Examples
As discussed earlier, there are different laws or rules defined for exponents. The important laws of exponents are given below:
- $a^m *a^n=a^{m+n}$
- $\frac{a^m}{a^n}=a^{m-n}$
- $(a^m)^n=a^{mn}$
- $\frac{a^n}{b^n}=(\frac{a}{b})^n$
- $a^0=1$
- $a^{-m}=(\frac{1}{a})^m$
- $a^\frac{1}{n}=\sqrt[n]{a}$
| Key words | Defintions |
|---|---|
| Exponents | a number or letter written above and to the right of a mathematical expression called the base. |
| Variable | a quantity that may be changed according to the mathematical problem |