Simplifying Exponential Expressions

Simplifying Exponents

Dr. Tom Giles

Exponent Properties

When multiplying powers add the exponents

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Multiple Choice

Simplify the following expression using exponential notation.

$$2^2\cdot2^4$$  

• $$2^8$$  

• $$2^6$$  

• $$4^6$$  

• $$4^8$$  

Exponent Properties

When you have a power of a power, multiply the exponents

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Multiple Choice

(x³)⁴

• x¹²

• x^-1

• x⁷

• x⁰

Exponent Properties

When you have a power of a product, distribute the exponent.

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Multiple Choice

Simplify: (3x²)³

• 27x⁶
• 9x⁶
• 3x⁶
• 9x⁵

Exponent Properties

When you have a quotient of powers, subtract the exponent.

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Multiple Choice

$$Simplify\ \ \frac{x^8}{x^2}$$  

• $$x^4$$  

• $$x^6$$  

• $$6x$$  

Exponent Properties

When you have a negative exponent, take the reciprocal to make positive.

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Multiple Choice

Rewrite using a positive exponent.
7^-10

• ¹/_7¹⁰
• 7¹⁰
• ¹/_7^-10
• -70

Multiple Choice

Simplify the expression: 
c⁴⋅c³=

• ^c12
• c⁴⁺³
• c⁷

Multiple Choice

Simplify the expression: 3x²⋅x²=

• 3x
• 3x²⁺²
• 3x⁴

Multiple Choice

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

• add
• subtract
• multiply
• divide

Multiple Choice

Simplify 4^-2= 

• 1/16
• -16
• 1/4
• -42

Multiple Choice

Multiple Choice

Multiple Choice

Multiple Choice

Anything raised to a power of zero is always: 

• 0

• 1

• itself

• negative

Multiple Choice

(5³x²y⁴)⁰

• 5xy

• 1

• 0

• 5

Multiple Choice

Simplify

(2a²b⁴z)(6a³b²z⁵)

• 8a⁵b⁶z⁶

• 12a⁶b⁸z⁵

• 12a⁵b⁶z⁶

• 8a⁶b⁸z⁵

Multiple Choice

(6x²)(-3x⁵)

• 18x⁷

• -18x⁷

• 18x⁷

• 3x⁷

Multiple Choice

When dividing powers with the same base, you _______________ the exponents.

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

Simplify

• x⁴/3

• 3x¹⁰

• 36x¹⁰

• 3x⁴

Multiple Choice

• 2 / x²

• -2x²

• 2x²

• 2x¹⁴

Multiple Choice

Simplify.  

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Multiple Choice

Multiple Choice

Simplify the expression shown. Your answer should contain only positive exponents.

• 16a¹²b¹⁴

Radical

Expressions​

• The opposite of a root is an exponent!

  ​To simplify SQUARE ROOTS:

  • Write the radicand as a product of numbers, one of which is a PERFECT SQUARE.

  • Find the square root of the perfect square.​

Radical Expressions

Basics/Square Roots

Multiple Choice

$$\sqrt[]{36}$$  

• 9

• 6

• 4

• 8

• NOT ALL SQUARE ROOTS ARE PERFECT!

  • When this happens you should follow the same process ,but you will need to leave any remaining products that cannot come out of the radical​ underneath the root.

Radical Expressions

Basics/Square Roots

Multiple Choice

$$\sqrt[]{18}$$  

• $$3\sqrt[]{2}$$  

• $$2\sqrt[]{9}$$  

• $$2\sqrt[]{3}$$  

• $$\sqrt[]{9}$$  

​Expon

Multiple Choice

$$\sqrt[3]{54}$$  

• $$3\sqrt[3]{18}$$  

• $$2\sqrt[3]{3}$$  

• $$3\sqrt[3]{2}$$  

• $$18\sqrt[3]{3}$$  

Multiple Choice

$$\sqrt[3]{64}$$  

• 32

• 4

• 8

• 2

Open Ended

What does B.I.T.E stand for?

Fractional Exponents can be written as radical expressions!

Bottom

Index

Top

Exponent​

Radical Expressions

Fractional Exponents

Multiple Choice

$$13^{\frac{1}{4}}$$  

• $$\sqrt[]{13}$$  

• $$\sqrt[4]{13}$$  

• $$\left(\sqrt[4]{13}\right)^2$$  

• $$3\sqrt[3]{2}$$  

Multiple Select

$$7^{\frac{3}{5}}$$ This fractional exponent can be written in TWO ways! Select two choices! 

• $$\left(\sqrt[3]{7}\right)^5$$  

• $$\left(\sqrt[5]{7}\right)^3$$  

• $$\sqrt[3]{7^5}$$  

• $$\sqrt[5]{7^3}$$  

Multiple Choice

Write the following as a radical expression: $$x^{\frac{3}{2}}$$  

(Be careful! ;)

• $$\sqrt[]{x^3}$$  

• $$\sqrt[2]{x^3}$$  

• $$\sqrt[3]{x^2}$$   

• $$\left(\sqrt[3]{x}\right)^2$$  

Multiple Choice

$$\sqrt[]{18}$$  

• $$3\sqrt[]{2}$$  

• $$2\sqrt[]{9}$$  

• $$2\sqrt[]{3}$$  

• $$\sqrt[]{9}$$  

• ​To simplify CUBE ROOTS:

  • Write the radicand as a product of numbers, one of which is a PERFECT CUBE.

  • Find the cube root of the perfect cube.​

Radical Expressions

Cube Root & Beyond