## 1.2 Learn Basic Properties and Operations

This lesson will help you learn the basic properties and rules that govern math problem-solving.

### Exponents

Numbers and variables with exponents are easy to work with if we follow the laws of exponents.

### The Laws of Exponents

**1.** To multiply numbers with the same base, add the exponents: $${a^m} \times {a^n} = {a^{m + n}}$$

### Examples

$${9^2}\cdot\,\,{9^3} = {9^{2 + 3}} = {9^5}$$$${3^4}\cdot \,\,{3^7} = {3^{4 + 7}} = {3^{11}}$$

**2.** To divide numbers with the same base, subtract the exponents: $${a^m} \div \;\,{a^n} = \;\,{a^{m - n}}$$

### Examples

$${4^5} \div {4^3} = {4^{5 - 3}} = {4^2}$$

**3.** To raise a number with an exponent to a power, multiply the exponents: $${({a^m})^n} = {a^{m \cdot n}}$$

### Examples

$${\left( {{7^2}} \right)^4} = {7^{2\,\cdot \,4}} = {7^8}$$$${\left( {{{10}^3}} \right)^7} = {10^{3\,\cdot \,7}} = {10^{21}}$$