Before we can do anything further with algebraic expressions, including multiplying or dividing monomials and polynomials, it’s critical that you know the **laws of exponents**. Of course, you could probably get away without knowing these laws formally, but then you wouldn’t have a strong foundation. A big part of your studies is being able to communicate your findings, both on paper and in speech. Thus, knowing the terminology will help tremendously.

We’ll use the laws of exponents mainly to simplify expressions, to make them easier to work with in later computations, such as solving equations containing exponents. The easiest of these laws to grasp are the **zero exponent rule** and **negative exponent rule**. The video below will explain what to do when you encounter *zero* and *negative exponents*.

The other exponent laws you will encounter are summarized underneath:

**Product rule:**

**Rule:**

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**Examples:**

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**You try:**

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(notice how the exponent **3** and **n** are **not** *like terms* so we leave it as 3 + n.

**Quotient rule:**

**Rule:**

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**Examples:**

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**You try:**

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(notice how the exponents **5n** and **2n** are *like terms*, so we subtract the *coefficients* only).

# Power of a power rule:

**Rule:**

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**Examples:**

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**Test:**

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(Students will commonly mistaken the power with multiplication, for example, multiply the exponent **3** by the base **3 **instead of 3 × 3 × 3 = 27)

A more thorough explanation of these laws are provided in the video:

Common error:nullStudents of all math backgrounds make this common mistake. Remember, you can only distribute the exponent

nif what’s inside the brackets is amonomial; x and y are two separate terms, hence a binomial. You could distribute thenin the following cases: nullIn the lesson to come, you will learn how to handle expressions like (x + y)² via a technique called

expanding. For a list of other common math errors, watch this link.

Now it’s time to put your knowledge of exponents to the test. The video below shows three complicated examples that require you use several of the exponent laws to simplify a single expression.