Exponent Rules Lesson (Honors)

Exponent Rules

• ​Product of Exponents

• Quotient of Exponents

• Zero Exponents

• Negative Exponents

Multiple Choice

How do you write
5⋅5⋅5⋅5⋅5⋅5⋅5
with an exponent?

• 5⁷
• 5⁶
• 7⁵
• 5

Anything to the power of zero = 1. Yes, anything. For real....anything.

​

​Zero Exponents

Multiple Choice

$$365^0=$$  

• 0

• 1

• 365

• $$\frac{1}{365}$$  

Multiple Choice

Simplify (-1/2)⁰

• 1
• 0
• -1
• -2

When powers are multiplied, add them.

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Product of Powers

Multiple Choice

The Product of Powers Property says when the base is the same and the exponent is different you should ________________________

• add the bases

• multiply the bases

• add the exponents

• multiply the exponents

Multiple Choice

Simplify: $$12^4\ \cdot\ 12^6$$  

• $$12^{10}$$  

• $$12^{24}$$  

• $$144^{10}$$  

• $$24^{10}$$  

Multiple Choice

Simplify: $$t^9\cdot\ t^8$$  

• $$t^1$$  

• $$t^{72}$$  

•   $$t^{17}$$  

• None of the above

Multiple Choice

Find the missing exponent: $$3^{16}=3^8\cdot3^?$$  

• 2

• 8

• Both 2 and 8 work

• None of the above

Multiple Choice

Simplify: $$7^8\cdot7$$  

•   $$7^9$$  

•   $$49^8$$  

• $$7^8$$  

• $$49^9$$  

Multiple Choice

Simplify:

$$\left(6x^2\right)\left(-3x^5\right)$$  

•   $$18x^7$$  

•   $$-18x^7$$  

• $$3x^7$$  

• None of the above

Multiple Choice

Simplify:

$$2m^4\cdot5m^2$$  

•   $$10m^6$$  

• $$10m^8$$  

•   $$7m^6$$  

• None of the above

Multiple Choice

Simplify:

$$c^5\cdot c^3\cdot c^3$$  

•   $$c^{45}$$  

•   $$3c^{11}$$  

•   $$c^{11}$$  

• None of the above

Multiple Choice

Simplify:

$$3x^2\left(-5x^4\right)$$  

• $$15x^2$$  

•   $$-15x^8$$  

• $$-2x^6$$  

• None of the above

When powers are raised to ANOTHER power, multiply them.

​

Product of Powers (part 2)

Multiple Choice

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

• add
• subtract
• multiply
• divide

Multiple Choice

$$\left(x^5\right)^4$$  

The power of a power rule says that when an exponential expression is raised to a power (as shown above), you should _________ the inner and outer exponents

• add

• subtract

• multiply

• divide

Multiple Choice

$$\left(x^7\right)^2$$  =

• $$x^{14}$$  

• $$x^9$$  

• $$x^5$$  

• $$2x^7$$  

Multiple Choice

Simplify: (r⁴)⁶

• 10r
• r¹⁰
• 24r
• r²⁴

Multiple Choice

• a⁷
• a¹⁰
• a³
• a^-3

Multiple Choice

Simplify the expression. Write your answer as a power.

$$\left(\left(-\frac{1}{3}\right)^5\right)^9$$  

• $$\left(-\frac{1}{3}\right)^{45}$$  

• $$\left(\left(-\frac{1}{3}\right)^9\right)^5$$  

• $$\left(-\frac{1}{3}\right)^{14}$$  

• $$\left(-\frac{1}{3}\right)^4$$  

Multiple Choice

Simplify (-3x⁴y⁵)²

• 9x⁸y¹⁰
• 6x⁸y¹⁰
• 3x⁸y¹⁰
• -9x⁸y¹⁰

Multiple Choice

Simplify:
(5ab²)²

• 25a²b⁴
• 10a²b⁴
• 5a²b⁴
• 25ab⁴

When powers are divided, SUBTRACT them.

Quotient of Powers

Multiple Choice

Quotient (Division) Rule states: keep the base the same and do this to the exponents.

• multiply

• add

• subtract

• divide

Multiple Choice

• x²
• x³
• x
• x⁵

Multiple Choice

• 2a⁴b⁴
• 4a³b⁴
• 4a⁸b⁵
• 2a⁴b³

Multiple Choice

• 4⁹
• 4⁴⁴
• 4²¹
• 4¹⁵

When powers are negative, FLIP them.

Negative Powers

Multiple Choice

Solve 5^-2

• -10
• 1/25
• 1/(5)²
• -1/10

Multiple Choice

3⁻⁴

• 1 ⁄ 81
• -81
• 81
• 1 ⁄ 12

Multiple Choice

7^-2

• 49
• 10/49
• -49
• 1/49

Multiple Choice

Solve (-8)^-2

• 1/(-8)²
• 1/8²
• 1/64
• -64

Multiple Choice

Simplify
x⁻⁶

• 1 ⁄ x⁶
• x⁶
• -x⁶
• -1 ⁄ x⁶

Multiple Choice

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

• add
• subtract
• multiply
• divide

Poll

Which laws do you not understand if any?  SELECT ALL THAT APPLY

• Yo Mrs. Flowers, I got this!

• Product Rule $$4^3\times4^2=4^{3+2}$$  

• Power Rule $$\left(4^2\right)^3=4^{2\times3}$$  

• Quotient Rule  $$\frac{4^5}{4^3}=4^{5-3}$$  

• Negative Rule  $$4^{-6}=\frac{1}{4^6}$$

Multiple Choice

Challenge:

How do you solve:
(2x⁵)(6x⁴)

• MULTIPLY coefficients
  MULTIPLY exponents
• DIVIDE coefficients
  SUBTRACT exponents
• Combine like terms
• MULTIPLY coefficients
  ADD exponents