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LESSON: Powers and Exponents

Site: MN Partnership for Collaborative Curriculum
Course: Mathematics Essentials Q1
Book: LESSON: Powers and Exponents
Printed by: Guest user
Date: Sunday, November 24, 2024, 7:16 AM

Description

Powers and Exponents

Table of contents

INTRODUCTION

Powers and Exponents

WATCH: Powers and Exponents

READ: Whole Numbers, Powers, Bases and Exponents

Whole Numbers, Powers, Bases and Exponents

In the past two lessons you have been working with whole numbers. A whole number is just that. It is a number that represents a whole quantity. Today, we are going to learn about how to use exponents. Exponents are very powerful little numbers. They change the meaning of the whole number as soon as they are added.

Here is an example.

The large number is called the base. (You can think about the base as the number that you are working with.)

The small number is called the exponent. (The exponent tells us how many times to multiply the base by itself.)

An exponent can also be known as a power.


We can read bases and exponents.

EXAMPLES:

3^5 is read as three to the fifth power.

2^7 is read as two to the seventh power.

5^9 is read as five to the ninth power.

We use the number with the power in all cases except two. When you see a base with an exponent of 2 or an exponent of 3, we have different names for those. We read them differently.

2^2 is read as two squared.

6^3 is read as six cubed.

It doesn’t matter what the base is, the exponents two and three are read squared and cubed.


What does an exponent actually do? An exponent tells us how many times the base should be multiplied by itself.

Examples:

7^3 = 7 \times 7 \times 7

5^{10} = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5

READ: Writing the Product of a Repeating Factor as a Power

Writing the Product of a Repeating Factor as a Power

In the last section, we took bases with exponents and wrote them out as factors. We can also work the other way around. We can take repeated factors and rewrite them as a power using an exponent.

Example

7 \times 7 \times 7 = \underline{\;\;\;\;\;\;\;}

There are three seven’s being multiplied. We rewrite this as a base with an exponent.

7 \times 7 \times 7 = 7^3


Example

11 \times 11 \times 11 \times 11 = 11^4


We can also find the value of a power by evaluating it. This means that we actually complete the multiplication and figure out the new product.


Example

5^2

We want to evaluate 5 squared. We know that this means 5 \times 5. First, we write it out as factors.

5^2 = 5 \times 5

Next, we solve it.

5^2 = 5 \times 5 = 25

RED ALERT!!! The most common mistake students make is to just multiply the base times the exponent.

5^2 IS NOT 5 \times 2

The exponent tells us how many times to multiply the base by itself.

5^2 is 5 \times 5


READ: Comparing Values of Powers

Comparing Values of Powers

We can also compare the values of powers using greater than, less than and equal to. We use our symbols to do this.

Greater than >

Less than <

Equal to =


To compare the value of different powers, we will need to evaluate each power and then compare them.


Example

5^3 \underline{\;\;\;\;\;\;\;}6^2

First, we can evaluate 5 cubed. 5^3 = 125

Next, we can evaluate 6 squared. 6^2 = 36

Now rewrite the problem.



One hundred and twenty-five is greater than thirty-six

EXAMPLE 1


EXAMPLE 2


CHECK Yourself! Exponents