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1.6: Evaluate Numerical and Variable Expressions Involving Powers

Difficulty Level: At Grade Created by: CK-12
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Practice Algebra Expressions with Exponents
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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.

5^4 + (-2)^4 + 12

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

6^3 + 5^2 + 25

Solution: 266

Example B

16(12^3)

Solution: 27,648

Example C

6^2 + 5^3 + 15 - 11

Solution: 165

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

5^4 + (-2)^4 + 12

First, Casey will need to evaluate the powers.

5^4 = (5)(5)(5)(5) = 625

(-2)^4 = (-2)(-2)(-2)(-2) = 16

Now we can substitute these values back into the expression.

625 + 16 + 12 = 653

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, 3^4 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 32^4 , 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 5b^4 + 17 . Let b=5 .

Solution

Step 1: Substitute 5 for “ b .”

5(5)^4 + 17

Step 2: Simplify the powers.

& 5(5 \cdot 5 \cdot 5 \cdot 5) + 17\\& 5(625) + 17

Step 3: Multiply then add to solve.

& 5(625) + 17\\& 3,125 + 17 = 3,142

The answer is 3,142.

Video Review

Khan Academy Level 1 Exponents

Explore More

Directions: Evaluate each power.

  1. 3^3
  2. 4^2
  3. (-2)^4
  4. (-8)^2
  5. 5^3
  6. 2^6
  7. (-9)^2
  8. (-2)^6

Directions: Evaluate each numerical expression.

  1. 6^2 + 22
  2. (-3)^3 + 18
  3. 2^3 + 16 - 4
  4. (-5)^2 - 19
  5. (-7)^2 + 52 - 2
  6. 18 + 9^2 - 3
  7. 22 - 3^3 + 7

Directions: Evaluate each variable expression using the given values.

  1. 6a + 4^2 - 2 , when a = 3
  2. a^3 + 14 , when a = 6
  3. 2a^2 - 16 , when a = 4
  4. 5b^3 + 12 , when b = -2
  5. 2x^2 + 52 , when x = 4

Vocabulary

Base

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 32^4, 32 is the base, and 4 is the exponent.
Evaluate

Evaluate

To evaluate an expression or equation means to perform the included operations, commonly in order to find a specific value.
Exponent

Exponent

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

Expression

An expression is a mathematical phrase containing variables, operations and/or numbers. Expressions do not include comparative operators such as equal signs or inequality symbols.
Integer

Integer

The integers consist of all natural numbers, their opposites, and zero. Integers are numbers in the list ..., -3, -2, -1, 0, 1, 2, 3...
Numerical expression

Numerical expression

A numerical expression is a group of numbers and operations used to represent a quantity.
Parentheses

Parentheses

Parentheses "(" and ")" are used in algebraic expressions as grouping symbols.
Power

Power

The "power" refers to the value of the exponent. For example, 3^4 is "three to the fourth power".
substitute

substitute

In algebra, to substitute means to replace a variable or term with a specific value.
Variable Expression

Variable Expression

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

Volume

Volume is the amount of space inside the bounds of a three-dimensional object.

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Date Created:

Dec 19, 2012

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Feb 26, 2015
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