To multiply two numbers with exponents, if the base numbers are the same, simply keep the base number and add the exponents.
Example 2
Multiply the following, leaving the answers with exponents.


To divide two numbers with exponents, if the base numbers are the same, simply keep the base number and subtract the second exponent from the first, or the exponent of the denominator from the exponent of the numerator.
Example 3
Divide the following, leaving the answers with exponents.


To multiply or divide numbers with exponents, if the base numbers are different, you must simplify each number with an exponent first and then perform the operation.
Example 4
Simplify and perform the operation indicated.

3^{2} × 2^{2} = 9 × 4 = 36

(Some shortcuts are possible.)
To add or subtract numbers with exponents, whether the base numbers are the same or different, you must simplify each number with an exponent first and then perform the indicated operation.
Example 5
Simplify and perform the operation indicated.

3^{2} – 2^{3} = 9 – 8 = 1

4^{3} + 3^{2} = 64 + 9 = 73
If a number with an exponent is raised to another power (4^{2})^{3}, simply keep the original base number and multiply the exponents.
Example 6
Multiply and leave the answers with exponents.

