Application of Laws of Exponents

PRODUCT RULE

Objective: Multiply exponential expressions with the same base.

Math Response

WARM-UP: What does 3³ equal?

Type answer here

Correct Answer: 27

Deg^°

Rad

​EXPONENTS

​2³

​base

​exponent

​2³ means 2 x 2 x 2

​4 x 2

​8

Special Case Exponents

Any BASE to the power of 1 simply equals the BASE.

​Example: 6¹ =

Example: y¹=

​​

If there is no exponent, there is an invisible 1​

Example: x = x¹

Example: 45 = 45¹ ​

Multiple Select

Which statements below are true?

• x¹ = x

• x⁰ = x

• 7¹ = 1

• 120⁰ = 1

• m⁰ = 1

PRODUCT RULE

EXAMPLES

​a^x ⋅ a^y = a^x+y

a² ⋅ a⁵ = a ⋅ a ⋅ a ⋅ a ⋅ a ⋅ a ⋅ a =

​

y¹⁴ ⋅ y⁵ ⋅ y³ =

​

Math Response

Simplify: y³ × y⁶ × y⁴

Type answer here

Correct Answer: y^{13}

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Rad

PRODUCT RULE NOTES

1) Bases have to be the same

​a^x ⋅ a^y = a^x+y

p⁴ ⋅ p³ =

2) Rule applies with multiplication (product)

x² ⋅ x⁶ =

x² + x⁶ =

x⁴ ⋅ x⁴ =

x⁴ + x⁴ =

but

p⁴ ⋅ x³ =

EXAMPLE

Simplify: 3x⁴ ⋅ -4x⁶

​

FIRST: What does it mean? (expanded form)​

​

​

SECOND: Simplify the expanded form.​

​

Math Response

Simplify: 2x⁴ ⋅ 6x³

Type answer here

Correct Answer: 12x^7

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Rad

EXAMPLE

Simplify: a²b⁴c² ⋅ a⁴c³

​

FIRST: What does it mean? (expanded form)​

​

​

SECOND: Simplify the expanded form.​

​

Math Response

Simplify: x³y⁴ ⋅ x⁶y²

Type answer here

Correct Answer: x^9y^6

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Rad

EXAMPLE

Simplify: -5a³b⁴ ⋅ -9ab⁴

​

FIRST: What does it mean? (expanded form)​

​

​

SECOND: Simplify the expanded form.​

​

Multiple Choice

Simplify: -2q⁴r²s⁵ × 4r⁶s³

• -8q⁴r⁸s⁸

• -6q⁴r⁸s⁸

• 2q⁴r⁸s⁵

• -8q⁴r¹²s¹⁵

• -8q⁴r¹²s⁸

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