Power, Quotient, Product Rule

Power, Quotient, and Product Exponent Rules

Power to a Power Rule

When raising an exponent to another exponent

1. Keep the Base

2. Multiply the exponents

EXAMPLE: (x^m)ⁿ = x^mn

Multiple Choice

According to the exponent rules, when we raise the exponents to another power, we _________ the exponents.

• Add

• Multiply

• Subtract

• Divide

Multiple Choice

Simplify the following expression to a single power:

$$\left(10^3\right)^8$$

• $$10^{11}$$

• $$80^3$$

• $$110^3$$

• $$10^{24}$$

Multiple Choice

Simply the following expression to a single power:

$$\left(10^{20}\right)^2$$

• $$10^{40}$$

• $$2000^2$$

• $$200^2$$

• $$10^{22}$$

Quotient Rule

When dividing exponents with the same base

Multiple Choice

According to the exponent rules, when we divide expressions, we _________ the exponents

• Add

• Multiply

• Subtract

• Divide

Multiple Choice

Simplify this expression to a single power.

$$\frac{2^{10}}{2^4}$$

• $$2^6$$

• $$2^{40}$$

• $$2^{14}$$

• $$\frac{2^{10}}{16}$$

Multiple Choice

Simplify this expression to a single power.

$$\frac{5^{15}}{5^2}$$

• $$5^{17}$$

• $$5^{13}$$

• $$5^{30}$$

• $$5^{20}$$

Product Rule

When multiplying exponents with the same base

Multiple Choice

According to the exponent rules, when we multiply expressions, we _________ the exponents

• Add

• Multiply

• Subtract

• Divide

Multiple Choice

Simplify this expression to a single power.

$$x^3\ x^6$$

• $$x^9$$

• $$x^{18}$$

• $$x^3$$

• $$x^6$$

Multiple Choice

Simplify this expression to a single power.

$$7^6\ 7^4$$

• $$7^6$$

• $$7^4$$

• $$7^{10}$$

• $$7^{24}$$