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# Evaluating Exponential Expressions

## Evaluate numbers raised to positive, negative, and fractional powers

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Practice Evaluating Exponential Expressions
Progress
Estimated12 minsto complete
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Evaluating Exponential Expressions

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.

### Guidance

When evaluating expressions we must keep in mind the order of operations. You must remember PEMDAS:

1. Evaluate inside the Parentheses.
2. Evaluate Exponents.
3. Perform Multiplication and Division operations from left to right.
4. Perform Addition and Subtraction 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.

### Vocabulary

• When evaluating expressions we must keep in mind the order of operations. You must remember PEMDAS:
1. Evaluate inside the Parentheses.
2. Evaluate Exponents.
3. Perform Multiplication and Division operations from left to right.
4. Perform Addition and Subtraction operations from left to right.

### Guided Practice

Evaluate the following expression for .

Solution:

### Practice

Evaluate the following expressions to a single number.

1. , if and
2. , if and
3. , if and
4. , if and
5. , if and