# Pre-Algebra : Power Rule of Exponents

## Example Questions

### Example Question #11 : Power Rule Of Exponents

Simplify:

Explanation:

Distribute the exponent of 2 to each term:

Multiply the corresponding exponents:

### Example Question #12 : Power Rule Of Exponents

Simplify:

Explanation:

The general rule for taking a power to a power is just that you multiply the exponents. So for you'd just multiply .

### Example Question #71 : Polynomials

Simplify the following expression:

Explanation:

When there is a product inside parenthesis and everything in the parenthesis is raised to a power, each term inside the parenthesis is taken to that power. If the terms inside the parenthesis are already raised to a power, multiply the exponents.

### Example Question #11 : Power Rule Of Exponents

Combine the expression into the least amount of bases and powers:

Explanation:

The power rule of exponents states that . In other words, one base "a" to two different powers is equal to "a" with its exponent being the product of those two powers.

Start from the middle and keep track of each power.

Change to a positive exponent. :

### Example Question #71 : Polynomials

Simplify the following expression:

Explanation:

First, the zero-exponent rule states that anything raised to the zero power is equal to :

Next, use the power rule (to raise a power to a power, multiply the exponents) to simplify the  and  variable-containing terms. This gives the expression in its simplest form:

### Example Question #11 : Power Rule Of Exponents

Simplify this expression:

Explanation:

When an exponent is raised to another power or another exponent we multiply them together. This is called the power rule. .

Everything within the parenthesis is raised to the power of three.

### Example Question #71 : Polynomials

Solve the equation.

Explanation:

When solving and exponent question first look at the sign in the equation.

When it's multiplication you have to add the exponents.

The base number in this case is 4. If the base number is the same leave it be and take it with you to the answer, if it is different then you have to do what the sign says. So in this case if they were different bases you would have to multiply them, however they are the same so take the 4 to the answer and add the exponents.

### Example Question #12 : Power Rule Of Exponents

Simplify:

Explanation:

One way to solve this question is to write out the terms in this expression.

With the exponent rule, notice that  can also be written as:

### Example Question #11 : Power Rule Of Exponents

Solve:

Explanation:

Multiply the coefficients together.

Multiply .  When multiplying powers of the same base, their powers can be added.

### Example Question #14 : Power Rule Of Exponents

Combine to one term: