In these lessons, we will learn five rules of exponent and how to use them. These exponent rules are typically covered in Grade 7 Math.

**Related Pages**

Exponents

Rules Of Exponents

Logarithmic Functions

More Math Lessons

The following table give the Exponent Rules. Scroll down the page for examples and solutions.

The rules of exponent are:

**Product Rule:**

When we multiply two powers that have the same base, add the exponents.

3^{2} x 3^{5} = 3^{7}

**Power Rule:**

When we raise a power to a power, multiply the exponents.

(3^{2})^{5} = 3^{10}

**Quotient Rule:**

When we divide two powers with the same base, we subtract the exponents.

3^{6} ÷ 3^{2} = 3^{4}

**Zero Rule:**

Any nonzero number raised to the power of zero equals 1.

54^{0} = 1

**Negative Rule:**

Any nonzero number raised to a negative power equals its reciprocal raised to the opposite positive power.

2^{-3} = 1/(2^{3})

**Introduction To Exponent Rules**

**Exponent Rules Song**

Learn exponent rules through music!

**Basic Exponent Properties**

This video will illustrate the rules with a few examples.

**Simple Rules Of When To Add Or Multiply The Exponents In Common Bases**

**Rules Of Exponents Set To Music**

**How To Apply The Rules Of Exponents?**

**Example:**

Simplify the following expressions:

a) (2x^{3}^{4})(3xy^{5})^{2}

b) (x^{5}y^{9})(-5x^{2}y^{2})^{4}

**Example:**

Simplify the following expressions:

a) (x^{2}/2)^{4}

b) (4n^{6})^{2}

**Example:**

Simplify the following expressions:

a) (3x^{2}y^{4})^{5}/(3x^{3}y^{7})^{3}

b) (5xy^{2})^{4}/(5x^{2}y)^{6}

**How To Evaluate Expressions With Negative Exponents?**

**Example:**

Simplify the following expressions:

a) (8a^{6}b^{-4})/(24a^{-8}b^{9})

b) (10a^{2}b^{6})(50a^{-3}b^{-4})

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