1.2 Learn Basic Properties and Operations

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

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