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

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