High School Math : Exponents

Example Questions

Example Question #1 : Multiplying And Dividing Exponents

Solve for

Cannot be determined from the given information.

Explanation:

Rewrite each side of the equation to only use a base 2:

The only way this equation can be true is if the exponents are equal.

So:

The  on each side cancel, and moving the to the left side, we get:

Example Question #1 : Simplifying Exponents

Solve for .

Explanation:

First, set up the equation: . Simplifying this result gives .

Example Question #2 : Simplifying Exponents

What is the largest positive integer, , such that  is a factor of ?

16

8

10

20

5

16

Explanation:

. Thus,  is equal to 16.

Example Question #3 : Simplifying Exponents

Order the following from least to greatest:

Explanation:

In order to solve this problem, each of the answer choices needs to be simplified.

Instead of simplifying completely, make all terms into a form such that they have 100 as the exponent.  Then they can be easily compared.

, , and .

Thus, ordering from least to greatest: .

Example Question #4 : Simplifying Exponents

Simplify the expression:

Cannot be simplified

Explanation:

Begin by distributing the exponent through the parentheses. The power rule dictates that an exponent raised to another exponent means that the two exponents are multiplied:

Any negative exponents can be converted to positive exponents in the denominator of a fraction:

The like terms can be simplified by subtracting the power of the denominator from the power of the numerator:

Example Question #1 : Solving And Graphing Exponential Equations

What are the y-intercepts of this equation?

Explanation:

To find the y-intercepts, set the  value equal to  and solve.

Example Question #2 : Solving And Graphing Exponential Equations

What are the horizontal asymptotes of this equation?

There are no horizontal asymptotes.

Explanation:

When looking for the horizontal asymptotes, examine the exponents of the variables. Because the variable in the denominator has a higher exponent than the variable in the numerator, the horizontal asymptote will be at .

Example Question #3 : Solving And Graphing Exponential Equations

What are the vertical asymptotes of the equation?

Explanation:

To find the vertical asymptotes, set the denominator equal to zero and solve.

However, we need to rationalize from here. We need to get rid of the cubed root in the denominator.

Therefore:

Bring the exponent from the numerator under the radical:

Simplify:

Example Question #4 : Solving And Graphing Exponential Equations

What is the horizontal asymptote of this equation?

There is no horizontal asymptote.

Explanation:

To find the horizontal asymptotes, we compare the exponents of  in our fraction. Because the denominator variable's exponent is greater than the numerator variable's exponent, our horizontal asymptote is at .

Example Question #5 : Solving And Graphing Exponential Equations

What are the vertical asymptotes of the equation?