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.

### Watch This

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