Example Questions

Example Question #711 : Algebra

Simplify .      Explanation:

This is just a matter of simply distributing this multiplication. Start by the basic distribution: Now, you just add the exponents that are similar. Thus, you get: Example Question #712 : Algebra

Simplify the following:   None of these   Explanation:

The rule for multiplying exponents is .

Using this, we see that .

Thus, our answer is .

Example Question #21 : Exponential Operations

The expression is equivalent to which of the following?    None of these Explanation:

The formula for multiplying exponents is .

Using this, we see that , and .

Example Question #22 : Exponential Operations

Simplify the following:       Explanation:

When two variables with exponents are multiplied, you can simplify the expression by adding the exponents together. In this particular problem, the correct answer is found by adding the exponents 5 and 5, yielding .

Example Question #23 : Exponential Operations

Simplify the following to its simplest exponential expression:       Explanation:

When multiplying exponential expressions, the bases remain the same and the exponents are added. Thus, the answer to this question is .

Example Question #24 : Exponential Operations can be written as which of the following?

A. B. C. A only

A, B and C

B and C

A and C

C only

A and C

Explanation:

B is not equivalent because... A is equivalent because of a property of exponents meaning that . Consequently, C is simply computing .

Example Question #25 : Exponential Operations

Solve when and .     Explanation:

Substitute for and for  Simplify:  Example Question #26 : Exponential Operations

What is ?     Explanation:

When an exponent is raised to an exponent, you may simplify by multiplying the exponents together to make a new exponent. In this case, becomes , which equals .

Example Question #27 : Exponential Operations

Simplify:      Explanation:

When exponents with the same base are being multiplied, you may add the exponents together to create a new exponent.

In this case, you would add 6 and 4 to create 10 as the new exponent.

Keeping the same base, the answer becomes .

Example Question #28 : Exponential Operations

Solve: when and .     Substitute for and for  .
Simplify:   