Power Rule of Exponents - Pre-Algebra

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.

Multiply the coefficients together.

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

The answer is:

To simplify this, first convert the second term to a negative exponent.

Since similar bases are multiplied, their powers can be added.

Solve by eliminating the parentheses first. When powers of the same base are multiplied, the powers can be added.

Combine like-terms.

Solve the parentheses first.

Simplify the third and fourth terms.

Combine or add the two terms.

When solving a division exponent question if the base is the same take it to the answer and then subtract the exponents.

In this case the bases are different so you must divide the bases then subtract the exponents.

Divide the bases:

Subtract the exponents:

The answer is

Simplify the numerator first.

When dividing similar bases, their powers can be subtracted.

When similar bases are multiplied, their powers can be added together.

The next step is to eliminate the negative exponent.

Remember that a value to a negative power is one over that value to its positive power. Write the following rule:

Apply this rule for .

Multiply the whole number with the numerator.

Since every base of a certain power is all multiplied, the powers of the similar bases can be added.

Reorganize the terms.

Simplify the bases.

Add the powers to get the answer.

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

When solving a negative exponent question simply do the reciprocal of the fraction and change the sign of the exponent.

is really .

Recipricol means flip, so;

Then change the sign of the exponent.

When you raise a power to a power, you multiply the two powers together. So,

We can also look at it like this:

When you have the same base and you raise a power to a power, you multiply the exponents. So,

If you are raising a power to another power, you simply multiply the powers together. So,

When raising a power to a power, we multiply the exponents. In this case, we get

And since they have different bases, we cannot combine them any further.

19 is the base number. It is the same on both sides.

If the base is the same on both sides and it is a multiplication problem we keep the base and add the exponents together.

The power rule for exponents states that when you raise a power to a power, you multiply the exponents, keeping the base the same. So,

can be written as

Since we cannot combine two different bases, this is now in simplest form.

In order to solve this problem you must take every integer and variable to the power of 2 like so,