(Negative/Zero Exponents) Properties of Exponents

Match

Warmup: Match the following. (Hint look at 4.2 notes)

• Power of Power

• Product of Powers

• Quotient of Powers

multiply/distribute

(x⁵)⁷

add

x⁵ * x⁷

subtract

x⁵/x⁷

• multiply/distribute

  (x⁵)⁷

• add

  x⁵ * x⁷

• subtract

  x⁵/x⁷

Open Ended

Warmup: Answer the following questions.

1. Simplify (3⁷)².

2. Simplify (4m²)⁵. (Hint: You have to give 4 an exponent of 1)

3. identify the radicand, exponent and index of (5x)^5/7.

Open Ended

Notice and Wonder: What does this say about both answers?

When there's a negative exponent, move the base to the other side of a fraction and change it into a positive exponent.
(Add this to your notes if it helps you remember)

Negative Exponents

Multiple Choice

Rewrite using a positive exponent.
(-5)^-4

• (-5)⁴
• ¹/_(-5)^-4
• ¹/_(-5)⁴
• -625

Multiple Choice

Rewrite using a positive exponent.
g^-7

• ¹/_g⁷
• g⁷
• ¹/_g^-7
• -g⁷

Multiple Choice

Rewrite each expression with a negative exponent.
¹/_(-5)⁷

• (-5)⁷
• ¹/_(-5)^-7
• (-5)^-7
• ¹/_78,125

Multiple Choice

Simplify with POSITIVE exponents.
s^-5 ⋅ s^-2

• s^-3
• ¹/_s⁷
• s^-7
• ¹/_s³

Multiple Choice

Write 8^-2/3 with positive exponents.

• 8^2/3

• 1/8^(-2/3)

• 1/8^2/3

• 8^(-3/2)

Open Ended

Notice and Wonder:

What's the difference between these two?

REMEMBER: if there is parentheses, you keep them together.

If there is NO parentheses, you separate them.

NOTE: If there are variables/constants that have positive exponents, they stay where they are.
(add to notes if needed)

Negative Exponents (cont.)

Multiple Choice

 Rewrite using positive exponents.

$$x^2y^{-2}$$

• $$x^2y^2$$  

• $$-x^2y^2$$  

• $$\frac{1}{x^2y^2}$$  

• $$\frac{x^2}{y^2}$$  

Multiple Choice

Rewrite using positive exponents.

$$7a^{-5}b^3$$  

• $$\frac{7a^5}{b^3}$$  
  

• $$\frac{b^3}{7a^5}$$  
  

• $$\frac{7}{a^5b^3}$$  
  

• $$\frac{7b^3}{a^5}$$  
  

Multiple Choice

Rewrite using positive exponents.

$$2a^{-2}b^{-3}c^4$$  

• $$\frac{2}{a^2b^3c^4}$$  

• $$\frac{2c^4}{a^2b^3}$$  

• $$\frac{c^4}{2a^2b^3}$$  

• $$2a^2b^3c^4$$  

Zero Exponent

Anything to the zero exponent is equal to 1!!

Rule: a⁰=1, where "a" is any real number, meaning any number.

EX:
a. 13459128⁰ = 1

b. ax⁰ = a ⋅ x⁰ = a ⋅ 1 = a, since it doesn't have parentheses

1

Multiple Choice

What does anything to the zero power equal??

• 0
• 1
• the variable

Multiple Choice

Simplify y⁰

• y

• 0

• 1

Multiple Choice

5⁰ ∙ 2⁰

• 0

• 1

• 10

Multiple Choice

Simplify -4x⁰

• -4
• 1
• -1

Multiple Choice

Simplify.

xy⁰

• xy

• x

• 1

Multiple Choice

Simplify.:

$$\left(2a^3\right)^0$$  

• 0

• $$2a^3$$  

• 1

Multiple Choice

Rewrite this expression with a negative exponent.
¹/_12⁴

• ¹/_12^-4
• 12⁴
• ¹/_20,736
• 12^-4

Multiple Choice

Which expression would be equivalent to $$2^{-6}$$ ?

• $$2^3\cdot2^3$$

• $$\left(2^3\right)^{-2}$$

• $$\frac{2^{10}}{2^4}$$

• $$2^6$$

Multiple Choice

Write as a single power: $$\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}$$

• $$2^{-3}$$

• $$2^3$$

• $$3^2$$

• $$3^{-2}$$

Dropdown

Rate your understanding for all properties. Refer to the vocabulary on your notes.

1 being I totally have no idea how to do this and

5 being this is easy I can teach someone else.

a. Product of Powers ​

Select answer

b. Quotient of Powers ​

Select answer

c. Negative Exponent ​

Select answer

d. Zero Exponent​

Select answer