Properties of Exponents
Exponential notation is a shorthand way of writing repeated
multiplication of the same number.
For example, 5^{3} is a shorthand way of writing 5
Â· 5 Â· 5.
In the expression 5^{3}:
â€¢ The base, 5, is the repeated factor.
â€¢ The exponent, 3, is the number of times the base appears as a factor.
An exponent is also called a power.
An exponent is not always a positive real number. Here is the definition of
a negative exponent:
Using this definition, we can show that:
Example 1
Write without using a negative exponent and then simplify: 6^{3 }
Solution
Note
The sign of the exponent does not indicate
the sign of the number.
For example, 6^{3} has a negative exponent,
3. But it simplifies to a positive number.
As another example, 3^{2} has a positive exponent. But it simplifies to a negative
number:
3^{2}= 3 Â· 3 = 9
Example 2
Write without using a negative exponent: 8wy^{2}.Solution
