Properties of Integer Exponents: Product & Quotient Rules

How to say a power aloud

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Identify the base:

$$4^3$$  

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Identify the exponent:  $$4^3$$  

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Identify the exponent:  $$5^2$$  

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Identify the base:  $$5^2$$  

Multiple Choice

Which number is the EXPONENT?
4^{2 =} 16

• 4
• 2
• 16

Multiple Choice

Which number is the BASE?
2³ = 8

• 2
• 3
• 8
• not here

Multiple Choice

Which is equivalent to 4 x 4 x 4 x 4 x 4

• 4⁶
• 5⁴
• 4⁴
• 4⁵

Multiple Select

Which equations with exponential expressions are true

• 3² = 3 • 3

• 4⁴ = 4 • 4

• 5⁴ = 4 • 4 • 4 • 4 • 4

• 7 • 7 • 7 • 7 • 7 • 7 = 7⁶

• 9³ = 9 • 9 • 9

Multiple Choice

What is the correct expanded form of

$$a^2$$  ?

• a

• a x a

• a x a x a

• a x a x a x a

Product Rule, Quotient Rule, and combining them

Product Rule

• Look at the right and see what happens when you multiply powers that have the same base

• When you expand 3² you have two 3s being multiplied and when you expand 3³ you have three 3s being multiplied.

• All together how many 3s are you multiplying?

Product Rule Short Cut?!!

When you multiply same base powers you keep the base and add the exponents.

x² * x⁷ = x²⁺⁷ = x⁹

Multiple Choice

Simplify the following:

$$a^{11}\cdot a^2\cdot a^0$$  

• $$a^{13}$$  

• $$1$$  

• $$a^{22}$$  

• $$a^0$$  

Multiple Choice

Practice: Use the product rule to simplify:

$$b^4\cdot b^2$$  

• $$b^8$$  

• $$b^{16}$$  

• $$b^6$$  

Multiple Choice

Product Rule

When multiplying exponents with the same base, _______ the exponents.

• subtract

• add

• multiply

• divide

Multiple Choice

$$4^1=$$  

• 4

• 0

• 1

Multiple Choice

$$4^0=$$  

• 4

• 0

• 1

Multiple Choice

$$10^3\cdot10^5=$$  

• $$10^3$$  

• $$10^5$$  

• $$10^8$$  

• $$10^{15}$$  

Multiple Choice

Simplify the expression.
x³x⁶

• x⁹
• x³
• x¹⁸
• x³⁶

Multiple Choice

According to exponent rules, when we multiply exponential expressions we _______ the exponents.

• add
• subtract
• multiply
• divide

Quotient Rule

• When dividing powers that have the same base think of dividing as the inverse of multiplying, so what is the inverse of adding?

• When you expand x⁵ you have five Xs being multiplied in the numerator and when you expand x² you have two Xs being multiplied in the denominator.

• So what happens when you have the Xs in the numerator and Xs in the denominator? Yup! you cross out the matching pairs!

• Now what did you end up with?

Quotient Rule Short Cut?!!

When you divide same base powers you keep the base and subtract the exponents.

x⁷ / x² = x^7-2 = x⁵

Multiple Choice

Simplify the following:

$$\frac{x^{16}}{x^2}$$  

• $$x^{14}$$  

• $$x^8$$  

• $$x^{18}$$  

• $$x^{-8}$$  

Multiple Choice

Simplify the following:

$$\frac{x^3}{x^8}$$  

• $$x^{-5}$$  

• $$x^5$$  
  

• $$x^{-3}$$  

• $$\frac{1}{x^{11}}$$  

Multiple Choice

Quotient Rule

When dividing exponents with teh same base, ________the exponents

• subtract

• divide

• add

• multiply

Multiple Choice

$$\frac{x^8}{x^5}$$  

• $$x^3$$  

• $$\frac{1}{x^3}$$  

• $$x^{13}$$  

• $$x^{40}$$  

Multiple Choice

Simplify the following:

$$\frac{x^{16}}{x^2}$$  

• $$x^{14}$$  

• $$x^8$$  

• $$x^{18}$$  

• $$x^{-8}$$  

Copy and Solve Using the Product Rule and Quotient Rule

Multiple Choice

Anything raised to a power of zero is always:

• 0

• itself

• 1

• negative

Multiple Choice

Simplify: 

$$\frac{k^4}{k^3}$$  

• $$k$$  

• $$k^7$$  

• $$k^{12}$$  

• $$\frac{1}{k}$$