What if you knew the volume of a cube was represented by the formula , where s the length of a side. You measure the cube's side to be 4 inches. How could you find its volume? After completing this Concept, you'll be able to evaluate exponential expressions like this one.
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CK-12 Foundation: 0103S Evaluate Algebraic Expressions with Exponents
For a more detailed review of exponents and their properties, check out the video at http://www.mathvids.com/lesson/mathhelp/863-exponents---basics.
Guidance
Many formulas and equations in mathematics contain exponents. Exponents are used as a short-hand notation for repeated multiplication. For example:
The exponent stands for how many times the number is used as a factor (multiplied). When we deal with integers, it is usually easiest to simplify the expression. We simplify:
However, we need exponents when we work with variables, because it is much easier to write than .
To evaluate expressions with exponents, substitute the values you are given for each variable and simplify. It is especially important in this case to substitute using parentheses in order to make sure that the simplification is done correctly.
Example A
The area of a circle is given by the formula . Find the area of a circle with radius .
Substitute values into the equation.
The area is approximately 907.92 square inches.
Example B
Find the value of , for and .
Substitute the values of and in the following.
Example C
The height of a ball in flight is given by the formula , where the height is given in feet and the time is given in seconds. Find the height of the ball at time .
Solution
The height of the ball is 12 feet.
Watch this video for help with the Examples above.
CK-12 Foundation: Evaluate Algebraic Expressions with Exponents
Vocabulary
- exponents : Exponents are short-hand notation for repeated multiplication. The exponent indicates the number of times to multiply the base by itself. For example: and
Guided Practice
Find the value of , for and .
Substitute the values of and in the following.
Explore More
Evaluate 1-8 using and .
For 9-10, use the fact that the volume of a box without a lid is given by the formula , where is a length in inches and is the volume in cubic inches.
- What is the volume when ?
- What is the volume when ?