# 1.6: Evaluate Numerical and Variable Expressions Involving Powers

**Basic**Created by: CK-12

**Practice**Algebra Expressions with Exponents

Do you know how to evaluate a numerical expression when it has powers in it? Casey is having a difficult time doing exactly that. When Casey arrived home from school he looked at his homework. He immediately noticed this problem.

Casey isn't sure how to evaluate this expression. Do you know how to do it? This Concept will show you how to evaluate numerical expressions involving powers. Then you will be able to help Casey at the end of the Concept.

### Guidance

Did you know that you can evaluate numerical and variable expressions involving powers? First, let's identify a numerical and a variable expression.

**
A
**
**
numerical expression
**

**is a group of numbers and operations that represent a quantity, there isn’t an equal sign.**

**
A
**
**
variable expression
**

**is a group of numbers, operations and variables that represents a quantity, there isn’t an equal sign.**

We can combine the order of operations, numerical expressions and variable expressions together with powers.

Let’s talk about powers.

**
A
**
**
power
**

**is a number with an**

*exponent***and a**

*base***. An**

*exponent***is a little number that shows the number of times a base is multiplied by itself. The**

*base***is the regular sized number that is being worked with.**

#### Example A

**
Solution:
**

#### Example B

**
Solution:
**

#### Example C

**
Solution:
**

Now let's go back to the dilemma at the beginning of the Concept. Here is the problem that was puzzling to Casey.

First, Casey will need to evaluate the powers.

Now we can substitute these values back into the expression.

**
This is the answer to Casey's problem.
**

### Vocabulary

- Numerical Expression
- A numerical expression is a group of numbers and operations used to represent a quantity.

- Variable Expression
- A variable expression is a mathematical phrase that contains at least one variable or unknown quantity.

- Power
- The "power" refers to the value of the exponent. For example, is "three to the fourth power".

- Base
- When a value is raised to a power, the value is referred to as the base, and the power is called the exponent. In the expression , 32 is the base, and 4 is the exponent.

- Exponent
- Exponents are used to describe the number of times that a term is multiplied by itself.

### Guided Practice

Here is one for you to try on your own.

Evaluate the expression . Let .

**
Solution
**

**
Step 1:
**
Substitute 5 for “
.”

**
Step 2:
**
Simplify the powers.

**
Step 3:
**
Multiply then add to solve.

**
The answer is 3,142.
**

### Video Review

Khan Academy Level 1 Exponents

### Explore More

Directions: Evaluate each power.

Directions: Evaluate each numerical expression.

Directions: Evaluate each variable expression using the given values.

- , when
- , when
- , when
- , when
- , when

### Image Attributions

## Description

## Learning Objectives

Here you'll evaluate numerical and variable expressions involving powers.