8.EE.A.1-Exponent Rules-Reteach

Exponent Rules Review Lesson/Practice

By Kristin Harrell

Rule #1

Products

​When you are multiplying the same bases, you add the exponents.

Ex. x²(x⁵) = x²⁺⁵ = x⁷​

Some text here about the topic of discussion

Multiple Choice

Simplify: $$x^{-4}\cdot x^2$$  

• $$x^{-2}$$  

• $$x^{-8}$$  

• $$x^2$$  

• $$x^8$$  

Multiple Choice

According to PRODUCT OF POWERS PROPERTY, what operation do you use to combine the exponents when the bases are the same?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

Evaluate: $$2^2\cdot2^5$$  

• 40

• 14

• 32

• 128

Rule #2

Quotient of powers property

​

When the same bases are being divided, you subtracat the exponents.

Example: x⁹/x⁴ = x^9-4 = x⁵

Example: x^-15/x² =x^-15-2 = x^-17​

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Multiple Choice

Evaluate: $$\frac{3^5}{3^2}$$  

• 3

• 1

• 9

• 27

Multiple Choice

$$\frac{x^?}{x^3}=x^8$$  

• 3

• 5

• 8

• 11

Rule #3

Power to a power​

When you have a power rasied to a power, you need to multiple.

Example: (x²)⁵ = x²⁽⁵⁾ = x¹⁰​

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Multiple Choice

Which of the following is equivalent to 2⁶?

• $$\left(2^{-3}\right)^{-2}$$

• $$\left(2^3\right)^3$$

• $$\left(2^{-3}\right)^2$$

• $$\left(2^{-3}\right)^{-3}$$

Multiple Choice

$$\left(x^2\right)^{?\ }=\ x^{12}$$  

• 6

• 10

• 14

• 24

Rule #4​

Exponent of 0​

Anytime you have an exponent of 0 your answer is 1!

Example: x⁰ = 1

Example: 10000⁰ = 1​

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Multiple Choice

$$y^0=$$  

• y

• 0

• 1

• 10

Multiple Choice

Simplify (-1/2)⁰

• 1
• 0
• -1
• -2

Multiple Choice

• 0
• 3
• 1
• -1

Rule #5

Negative Exponents

When you have negative exponents you need to use the reciprocal.

Example: x^-3 = 1/x³

Example: 1/y^-5 = y⁵

Some text here about the topic of discussion

Multiple Choice

Rewrite using a positive exponent.
7^-10

• ¹/_7¹⁰
• 7¹⁰
• ¹/_7^-10
• -70

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 using a positive exponent.
w^-13

• -w¹³
• ¹/_w¹³
• ¹/_w^-13
• w¹³

Multiple Choice

5³⋅5⁴

• 5⁷
• 5⁻¹
• 5¹²
• 5

Multiple Choice

c⁵ * c ³ * c³

• c⁴⁵
• 3c¹¹
• c¹¹
• 3c⁴⁵

Multiple Choice

(x⁴)²

• x⁸
• x⁶
• x²
• 8

Multiple Choice

(6x²)(-3x⁵)

• 18x⁷
• -18x⁷
• 18x⁷
• 3x⁷

Multiple Choice

Evaluate the expression using the quotient rule.

• x¹³
• x⁵
• x³⁶
• x^-5

Multiple Choice

Simplify the expression:
(5⁸) ÷ (5²)

• 5⁶
• 5¹⁰
• 5⁴
• 5¹⁶

Multiple Choice

Simplify the expression in exponential form:
134⁰

• 0
• 134
• 1

Multiple Choice

Simplify (2x⁴y⁷)³

• 6x⁷y¹⁰
• 6xy³²
• 8x¹²y²¹
• 8x⁷y¹⁰

Multiple Choice

Evaluate the expression using the quotient rule.

• 2¹⁴ z¹³
• 2²/z⁷
• 2¹⁴/ z⁷
• 2² z⁷

Multiple Choice

Simplify         m¹²/ m³

• m^12-3  = m⁹
• m^12/3  = m⁴
• m^-9
• -m⁹

Multiple Choice

  simplify    7^-2

• 1/7² = 1/49
• -49
• -14
• 1/14

Multiple Choice

According to exponent rules, when we raise a power to a power we _______ the exponents.

• add
• subtract
• multiply
• divide

Multiple Choice

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

• add
• subtract
• multiply
• divide

Multiple Choice

According to exponent rules, when we divide powers we _______ the exponents.

• add
• subtract
• multiply
• divide

Multiple Choice

5^-3 = 1

• True 
• False 

Multiple Choice

8⁰ = 0

• True 
• False 

Multiple Choice

7⁸/7⁴ = 7²

• True 
• False 

Multiple Choice

Simplify the expression.

• 1
• g¹⁰
• g²⁵
• g

Multiple Choice

Evaluate the expression using the quotient rule.

• 3⁴
• 1/3⁴
• 3^-12
• 3³²

Multiple Choice

True or False?

• True
• False

Multiple Choice

Anything raised to a power of zero is always: 

• 0
• 1
• itself
• negative

Multiple Choice

(2⁸)²

• 2¹⁶
• 2¹⁰
• 2⁶
• 2⁴

Multiple Choice

Simplify the following:

$$3x^2\ ⋅\ 2x^4$$

• $$6x^6$$

• $$5x^8$$

• $$6x^8$$

• $$9x^6$$

Explanation Slide...

Simplify the following:3x2 ⋅ 2x4 = 6x6When multiplying exponents with the same base:-Multiply the coefficients-ADD the exponents

Multiple Choice

Simplify the following:

$$(5x^5)^2$$

• $$25x^{10}$$

• $$25x^7$$

• $$10x^{10}$$

• $$10x^7$$

Explanation Slide...

Simplify the following:(5x5)2 = 25x10This is power of power rule:When taking an exponent to another power:-Coefficient gets the exponent (5^2 = 25)-multiply the exponents.

Multiple Choice

Simplify the following (CAREFUL!!!):

$$\frac{x^{12}}{x^{-2}}$$

• $$x^{14}$$  

• $$x^{-6}$$  

• $$x^{10}$$  

• $$\frac{1}{x^6}$$

Explanation Slide...

Quotient rule:= x12 - -2 = x14When dividing exponents with the same base, keep the base and SUBTRACT the exponents