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 = −24**

Use 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}**

^{3}· 6

^{5}=

0 out of 0 correct.