Product Power Property

Exponent Properties

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Review & Practice​

Poll

Pick the one with the exponent.

• $$x^2$$  

• $$x_2$$  

• $$2x$$  

• $$\log_2x$$  

​What is an Exponent?

• ​The exponent of a number says how many times to use that number in multiplication.

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• It is written as a small number to the right and above the base number.

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• In this example: 8² = 8 × 8 = 64

• (The exponent "2" says to use the 8 two times in a multiplication.)

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• Another example: 5³ = 5 × 5 × 5 = 125

• (The exponent "3" says to use the 5 three times in a multiplication.)

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• Other names for exponent are index or power.

Multiple Choice

Exponents are used to represent repeated __________

• addition

• subtraction

• multiplication

• division

Multiple Choice

Write each product using an exponent.  7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 

• 7⁷

• 7⁸

• 8⁷

• 7⁹

Multiple Choice

Write each product using an exponent.  4 x 4 x 4 x 4 x 4 

• 4⁵

• 5⁴

• 4⁶

• 4⁶

Multiple Choice

Find the value (number answer) of the power.  3³

• 9

• 6

• 27

• 12

​Product Rule for Exponents

​When Multiplying exponents with the same base

Imagine if we had to write it all out into standard form: ​

​

​becomes:

​Product Rule for Exponents

Short Cut:​

​When Multiplying exponents with the same base

1. ​Keep the Base

2. ​Add the Exponents

3. ​EX)

Multiple Choice

Simplify the expression:  c⁴⋅c³=

• $$c^{12}$$  

• c7

• c⁷

• $$c^1$$  

Multiple Choice

Simplify the expression: 3x²⋅x²=

• 3x

• 4x⁴

• 3x⁴

Multiple Choice

(3⁴)(3⁷)

• 3²⁸

• 3³

• 3^-3

• 3¹¹

• $$9^{11}$$  

Multiple Choice

(x⁸)(x^-5)

• x^-40

• x^-13

• x¹³

• x³

Multiple Choice

Simplify. Your answer should contain only positive exponents. $$x^2\cdot x^4$$  

• $$x^2$$  

• $$x^6$$  

• $$x^{-2}$$  

• $$x^8$$  

Multiple Choice

Simplify the expression: $$5x^9\cdot-6x^2$$  

• $$-30x^{11}$$  

• $$-30x^{18}$$  

• $$-x^{11}$$

• $$-x^{18}$$  

Multiple Choice

Simplify the expression: $$d^8\cdot d^{10}$$   

• $$d^2$$  

• $$d^{80}$$  

• $$d^{810}$$  

• $$d^{18}$$  

Multiple Choice

Simplify. Your answer should contain only positive exponents. $$2a^2b^3\cdot4ab^2$$  

• $$8a^3b^5$$  

• $$2ab^2$$  

• $$8a^2b^5$$  

• $$\frac{1}{2}ab$$  

Multiple Choice

Simplify the expression: $$\left(2m^4\right)\left(5m^2\right)$$  

• $$10m^6$$  

• $$10m^8$$  

• $$7m^6$$  

• $$7m^8$$  

​Power of a Product

​Power of a Product

Short Cut Rule:​

​When raising an exponent to another exponent

1. Keep the Base

2. Multiply the Exponents

3. ​Examples:

   1. ​(x^m)ⁿ=x^m*n

   2. ​(x⁴)⁵=x²⁰

​

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Multiple Choice

(2⁸)²

• 2¹⁶

• 2¹⁰

• 2⁶

• 2⁴

Multiple Choice

(r⁴)⁶

• 10r

• r¹⁰

• 24r

• r²⁴

Multiple Choice

(x²)⁶

• x¹²

• x⁸

• x²⁶

• x⁴

Multiple Choice

Simplify:

$$\left(4r^2\right)^4$$  

• $$4r^8$$  

• $$16r^8$$  

• $$4^4r^6$$  

• $$4^4r^8$$  

Multiple Choice

Simplify:

$$\left(2x^2y^3\right)^2$$  

• $$2x^4y^6$$  

• $$4x^4y^6$$  

• $$4x^4y^5$$  

• $$2x^4y^5$$  

Multiple Choice

Simplify:

$$\left(6x^4y^6\right)^3$$  

• $$6^3x^7y^9$$  

• $$18x^{12}y^{18}$$  

• $$6^3x^{12}y^{18}$$  

• $$6x^{12}y^{18}$$  

Multiple Choice

Simplify:

$$6x^2\cdot3x^5\cdot\left(xy\right)^3$$  

• $$18x^8y^3$$  

• $$18x^7xy^3$$  

• $$18x^{10}y^3$$  

• $$18x^{10}y^{ }$$