In other words, exponents are another way to write MULTIPLICATION.

Let’s illustrate this concept by  rewriting the product  (4)(4)(4) using exponential notation:

In this example, 4 represents the base and 3 is the exponent.  Since 4 was written three times in a product, then our exponent is 3.  We always write our exponent as a smaller script found at the top right corner of the base.

You can apply this idea in the other direction.  Let’s say you have it written in exponential notation and you need to evaluate it. The exponent will tell you how many times you write the base out in a product.  For example if you had 7 as your base and 2 as your exponent and you wanted to evaluate out you could  write it out like this: 

If you said 5, you are correct!

What is the exponent?

If you said 4, you are right!
 

Let’s rewrite it as multiplication and see what we get for an answer:

If you said 7, you are correct!

What is the exponent?

If you said 1, you are right!

Let’s rewrite it as multiplication and see what we get for an answer:

If you said 1/3, you are correct!

What is the exponent?

If you said 2, you are right!

Let’s rewrite it as multiplication and see what we get for an answer:

*Multiply
 

Please     Parenthesis or grouping symbols
Excuse    Exponents (and radicals)
My Dear   Multiplication/Division left to right
Aunt Sally  Addition/Subtraction left to right

*Exponent
*Multiply
*Add

So in this problem, the first thing we need to do is work the inside of the absolute value.  And then go from there.

*Exponent
 

*Add in num. and subtract in den.
 

Don't let the fact that it is a letter throw you. Since it represents a number, you treat it just like you do a number when you do various mathematical operations involving variables.

x is a very common variable that is used in algebra, but you can use any letter (a, b, c, d, ....) to be a variable.

2x + y, a/5, and 10 - r are all examples of algebraic expressions.

For example, the area of a rectangle is length times width.  Well, not every rectangle is going to have the same length and width, so we can use an algebraic expression with variables to represent the area and then plug in the appropriate numbers to evaluate it.  So if we let the length be the variable l and width be w, we can use the expression lw.  If a given rectangle has a length of 4 and width of 3, we would evaluate the expression by replacing l with 4 and w with 3 and multiplying to get a value of 4 times 3 or 12.

Let’s step through some examples that help illustrate these ideas.

*Exponent
*Multiply
*Add
*Subtract

*Multiply

*Add
 

Since we got a TRUE statement (7 does in fact equal 7), then 2 is a solution to this equation.

Since we got a FALSE statement (16 does not equal 14), then 5 is not a solution.

In that situation, you want to 

Example 11:    Write the phrase as an algebraic expression.

  The sum of a number and 10.

It looks like the only reference to a mathematical operation is the word sum.  So, what operation will we have in this expression? 

If you said addition, you are correct!!!

The phrase 'a number' indicates that it is an unknown number.  There was no specific value given to it.   So we will replace the phrase 'a number' with the variable x.  We want to let our variable represent any number that is unknown

Putting everything together, we can translate the given english phrase with the following algebraic expression:

Example 12:    Write the phrase as an algebraic expression.

The product of 5 and a number.

This time, the phrase that correlates with our operation is 'product' - so what operation will we be doing this time?   If you said multiplication, you are right on.

Again, we have the phrase 'a number', which again is going to be replaced with a variable, since we do not know what the number is.
 

Let’s see what we get for this answer:

The following are some key words and phrases that translate into an equal sign (=):

Example 13:    Write the sentence as an equation.  Let x represent the unknown number. 

The quotient of 3 and a number is ½.

'Is' will be replaced by the symbol =.

Let’s put together everything going left to right:

Example 14:    Write the sentence as an equation.   Let x represent the unknown number.

7 less than 3 times a number is the same as 0.

Do you remember what times translates into?   If you said multiplication, you are correct.

'Is the same as' will be  replaced by the symbol =.

Let’s put together everything going left to right:

To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that  problem.  At the link you will find the answer as well as any steps that went into finding that answer.