1.02 Evaluate exponents
Introduction
We have previously looked at exponents and how they can be written in exponential form, a^{b}, or expanded form, a \times a \times a..., as a product of factors. Now let's look at how to evaluate or simplify problems involving exponents.
Evaluating exponential expressions
A base to the power of any other number, e.g. 3^4, can be read as "3 to the power of 4", and means that the base number is multiplied by itself the number of times shown in the power.
3^4=3\times3\times3\times3
To evaluate or simplify the above exponential expression, the only step we need to take is completing the multiplication. The simplified product is the number in standard form.
| \displaystyle 3^4 | \displaystyle = | \displaystyle 3\times3\times3\times3 | |
| \displaystyle = | \displaystyle 81 | Simplify the multiplication |
The exponential expression 3^4 is evaluated to 81, the number in standard form.
Examples
Example 1
Evaluate 3^2.
Example 2
Evaluate \left(\dfrac{2}{5}\right)^4.
An exponent or power tells how many times a base number must be multiplied by itself.
To evaluate an exponential expression, expand the notation and perform the multiplication.