What if you had an exponential expression requiring multiple operations, like ? How could you simplify it? After completing this Concept, you'll be able to use the order of operations to evaluate exponential expressions like this one.
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Foundation: 02807S Evaluating Exponential Expressions
Guidance
When evaluating expressions we must keep in mind the order of operations. You must remember PEMDAS:
- Evaluate inside the Parentheses .
- Evaluate E xponents.
- Perform M ultiplication and D ivision operations from left to right.
- Perform A ddition and S ubtraction operations from left to right.
Example A
Evaluate the following expressions.
a)
b)
c)
d)
Solution
a) A number raised to the power 0 is always 1.
b)
c) Remember that an exponent of means taking the square root.
d) Remember that an exponent of means taking the cube root.
Example B
Evaluate the following expressions.
a)
b)
c)
Solution
a) Evaluate the exponent:
Perform multiplications from left to right:
Perform additions and subtractions from left to right:
b) Treat the expressions in the numerator and denominator of the fraction like they are in parentheses:
c)
Example C
Evaluate the following expressions for .
a)
b)
c)
Solution
a)
b)
c)
Watch this video for help with the Examples above.
CK-12 Foundation: Evaluating Exponential Expressions
Vocabulary
- When evaluating expressions we must keep in mind the order of operations. You must remember PEMDAS:
- Evaluate inside the Parentheses .
- Evaluate E xponents.
- Perform M ultiplication and D ivision operations from left to right.
- Perform A ddition and S ubtraction operations from left to right.
Guided Practice
Evaluate the following expression for .
Solution:
Practice
Evaluate the following expressions to a single number.
- , if and
- , if and
- , if and
- , if and
- , if and