Polynomials - Pre-Algebra

The product rule states that when two like bases with the same power are being multiplied, we add the powers together and preserve the base. In mathematical language, . If constants are present in front of either base we multiply them as usual.

Combine using the power rule:

Combine the parenthesis:

Factor fully:

The product rule of exponents states that we can multiply two exponents with the same base by adding the exponents. The exponents of different bases cannot be summed, therefore our term will not change.

Therefore, the simplest form of the expression is

which can be written as

When you multiply exponents with the same base, you add the exponents:

When you multiply exponents with the same base, you add the exponents:

When you multiply exponents with the same base, you add the exponents:

When you multiply exponents with the same base, you add the exponents:

When you multiply exponents with the same base, you add the exponents:

When you multiply exponents with the same base, you add the exponents:

When you multiply exponents with the same base, you add the exponents:

When you multiply exponents with the same base, you add the exponents:

When you multiply exponents with the same base, you add the exponents:

When you multiply exponents with the same base, you add the exponents:

When you multiply exponents with the same base, you add the exponents:

When you multiply exponents with the same base, you add the exponents:

Since the bases are all alike and are multiplied, the exponents can be added.

In mathematical terms:

Plugging in four as our base and the various exponents we get the following,

.

According to the power rule for exponents, if a quantity is raised to a certain exponent, the powers of the inner quantity can be multiplied with the power outside the parentheses.

Eliminate the negative exponent by the following rule:

The exponents can be multiplied in this case.

Expand out the terms to verify.

Simplify each parentheses before multiplying.

Recall the rules of exponents which states if exponents are being raised to another one they are multiplied and if like bases are being multiplied their exponents are added.

Applying these rules we get,

.

Evaluate the quantities inside the parentheses first. The powers are multiplied when they are bounded in the parentheses.

Combine like-terms.