Power Rule of Exponents - Pre-Algebra

When an exponent question is in this product form we need to multiply the exponents together.

The product rule of exponents states that when you're multiplying two powers with the same base, you add the exponents:

In this instance,

The "power rule" states that when you raise a power to a power, you mutiploy the exponents:

Recall the Power Rule of Exponents: .

To simplify the expression , use this rule to distribute the exponents:

Recall the following rules:

The Product Rule of Exponents says:

The Power Rule of Exponents says: __and

Step 1: Use the Power Rule of Exponents to distribute the exponents:

Step 2: Use the Product Rule of Exponents to simplify further:

Distribute the exponent of 2 to each term:

Multiply the corresponding exponents:

The Quotient of Powers Property states when you divide two powers with the same base, you subtract the exponents.

In this case, the exponents are 8 and 6:

Recall, to distribute exponents through a polynomial, you must multiply the exponents. Thus, our expression can be simplified as follows:

Recall the Power Rule of Exponents:

To simplify the expression , use this rule to distribute the exponents:

Recall the following rules:

The Product Rule of Exponents says:

The Power Rule of Exponents says: and

Step 1: Use the Power Rule of Exponents to distribute the exponents:

Step 2: Use the Product Rule of Exponents to simplify further:

First, distribute the exponent outside of the parentheses to each of the elements inside of the parentheses, including the 2.

Remember that in this case, when an exponent is raised to another power, the exponents multiply.

Now we need to mutiply that answer by the outside .

For this last step, remember that the exponents on the add.

The power rule of an exponent means that when two exponential expressions with the same base are multiplied, you add the exponents together. In this case,

can be thought of as a "string" of 24 variables being multiplied together, so by multiplying that string by another 2 variable units, you have seamlessly extended the chain by two units.

For , it is important to remember that the power rule does no apply during addition, so the exponent is applied first, then the exponential values are added following the order of operation, so the final expression is:

or

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

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.

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. :

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:

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.

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.

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:

Since both terms are multiplied, the powers of each base can be added or subtracted.

According to the rules of exponents,

Therefore, our terms can combine as follows.