# Beginning Algebra Tutorial I--Exponents and PEMDAS

## About Me

Hello and Welcome!!! My name is Patty. I am 37 years old, married, mother of four wonderful children, and recently awarded my Associates Degree in Computer Science.

While working towards my degree, Algebra was one of the hardest subjects for many students. In this tutorial, I will cover a brief introduction to some of the very basic rules of Exponents and the Order of Operations (PEMDAS).

I hope this tutorial serves as a review or helps those just learning this material for the first time. In the near future, I do plan on adding more advanced tutorials.

## Lesson One---Exponents

*****Note that this symbol **•** is often used as the multiplication symbol.

Exponents can seem intimidating to some. Exponents are used for repeated multiplication. For Example instead of saying **2 • 2 • 2 • 2 • 2 • 2**, the shorter way would be to use exponents in this case **2 ^{6}** or "two to the sixth power".

In the example above the **2** is the **base** number and the ** ^{6}** is the

**exponent**.

Another way exponents are shown is using this symbol **^** to show the base raised to a certain power.

**Examples:**

10would look like^{2}10 ^ 2.

xwould look like^{5}x ^ 5

Below is just some of the very basic rules which will be covered below.

In the chart below, the variable * x* is the base and

*and*

**n***are exponents.*

**m**## Very Basic Exponent Rules

## Exponent Rules Example One

**x ^{n}** Whatever

*is equal to, multiply that same number*

**x***amount of times.*

**n**## Exponent Rules Example Two

**x ^{0} = 1 Any** base raised to the 0 power is

**ALWAYS**equal to 1.

## Exponent Rules Example Three

**x ^{m} • x^{n} = x^{m + n}** As long as the variable is the same just add the exponents.

## Exponent Rules Example Four

**x ^{m} / x^{n} = x^{m - n}** As long as the variable is the same just subtract the exponents.

## Lesson Two--PEMDAS

Lets begin with the Order of Operations. When solving an equation or simplifying an expression, solve/simplify in this order:

**P**arenthesis (first solve what is in the parenthesis and/or brackets)**E**xponents (then evaluate the exponents ex. 2^{3 }= 2 x 2 x 2 = 8)**M**ultiply and/or**D**ivide (from left to right)**A**dd and/or**S**ubtract (from left to right)

One way I was taught to remember this rule:

"**P**lease **E**xcuse **M**y **D**ear **A**unt **S**ally!"

## PEMDAS Examples

In the examples below, I will attempt to show you how to solve the problems step-by-step.

## Problem 1: 5 ^ 2 • (10-8)

5^{2}• (10-8) = ?

- First solve what is in the
Parenthesis(10-8) = 2- Now we have
5^{2}• 2 = ?- Then Evaluate the
Exponent5^{2}= 5 • 5 = 25- Now we have
25 • 2 = ?- Finally
Multiply and solve:25 • 2 = 50

## Problem 2: (7 • 2) - [ 9 ÷ (8 ÷ 8) ]

(7 • 2) - [ 9 ÷ (8 ÷ 8) ] = ?

At first glance this problem may seem tricky. In this example, we work with the innermost parenthesis, the parenthesis inside the brackets.

- First solve what is in the innermost
Parenthesis(8 ÷ 8) = 1- Now we have
(7 • 2) - [ 9 ÷ 1] = ?- Then solve what is in the Brackets
[ 9 ÷ 1] = 9- Now we have
(7 • 2) - 9 = ?- Then solve what is in the
Parenthesis(7 • 2) = 14- Now we have
14 - 9 = ?- Finally
Subtract and solve:14 - 9 = 5

## Problem 3: (8 - 2 * 4 + 3 ^ 2) / 6 ( 2 - 1)

(8 - 2 • 4 + 3^{2})-------------- = ? 6(2 - 1)

This problem may seem a little overwhelming at first. With this type of problem, the fraction bar acts as a type of Parenthesis. We will start with simplifying the top and then the bottom.

- On the
topwe will start with theExponent3^{2}= 3 • 3 = 9- On the
topwe now have8 - 2 • 4 + 9 = ?- Now the
Exponent is gone we move toMultiplication2 • 4 = 8- On the
topwe now have8 - 8 + 9= ?- Reading from
lefttorightwe are left withSubtraction andAddition8 - 8 = 0- Now on the top we have
0 + 9 = 9- On the
topwe are left with9- On the
bottomwe have6 ( 2 - 1) = ?- First solve what is in the
Parenthesis(2 - 1) = 1- On the
bottomwe now have6 ( 1 )= 6•1 = 6*Note the Parenthesis act as a multiplication symbol.- On the
bottomwe are left with6- Now we combine the
topand thebottom9 / 6- Simplify the fraction and the final answer is
3 / 2

## Final Thoughts

I hope that this tutorial gave you a very basic understanding of the basic rules of Exponents as well as the Order of Operations, PEMDAS.

Take the test on the right to test what you have learned!! If you scored low at first...try, try again. Re-read this article, follow along with the samples provided and try the test again.

For those just learning, remember Math can be hard when first learned, but with practice and determination...Anything is possible!!!

Thank-you for taking the time to read this article. GOOD LUCK and NEVER GIVE UP!!!

If you like this tutorial, you may want to check out my next tutorial on Beginning Algebra Tutorial II--Evaluating Expressions and Solving Equations.

## Comments

OOH!,Patty! HAH-HAH! That is nice and informative. Many need to see it. I voted up,my friend.

Nice tutorial.

Problem 3: 8 - 2 * 4 + 3 ^ 2 / 6 ( 2 - 1)

You should enclose 8 - 2 * 4 + 3 ^ 2 inside parentheses to indicate that all of them are included in the numerator. Otherwise, only 3 ^ 2 would be considered to be on top of the fraction bar.