### Section 1: Basic Rules of Exponents

### It Is Important That You Watch This Video First

Exponents are used to show repeated multiplication. For example, 4^{3} means 4 · 4 · 4 = 64.

In this section, we will review basic rules of exponents.

**Product Rule of Exponents a ^{m}a^{n} = a^{m + n}**

When multiplying exponential expressions that have the same base, add the exponents.

* Example*:

Multiply:

4x^{3}· −6x^{2}

* Solution*:

Multiply coefficients:

4 · −6 = −24Use the product rule to multiply variables :

x^{3}· x^{2}= x^{3 + 2}= x^{5}

4x^{3}· −6x^{2}= −24x^{5}

**Quotient Rule of Exponents**

When dividing exponential expressions that have the same base, subtract the exponents.

* Example*:

Simplify:

* Solution*:

Divide coefficients: **8 ÷ 2 = 4**

Use the quotient rule to divide variables :

**Power Rule of Exponents (a ^{m})^{n} = a^{mn}**

When raising an exponential expression to a new power, multiply the exponents.

* Example*:

Simplify:

(7a^{4}b^{6})^{2}

* Solution*:

Each factor within the parentheses should be raised to the 2

^{nd}power:

(7a^{4}b^{6})^{2}= 7^{2}(a^{4})^{2}(b^{6})^{2}Simplify using the Power Rule of Exponents :

(7a^{4}b^{6})^{2}= 7^{2}(a^{4})^{2}(b^{6})^{2}= 49a^{8}b^{12}

*Test Your Knowledge by opening up the Test Yourself Activity.*