​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 ​

PRODUCT RULE

EXAMPLES

​a^x ⋅ a^y = a^x+y

a² ⋅ a⁵ = a ⋅ a ⋅ a ⋅ a ⋅ a ⋅ a ⋅ a =

​

y¹⁴ ⋅ y⁵ ⋅ y³ =

​

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

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

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SECOND: Simplify the expanded form.​

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EXAMPLE

Simplify: a²b⁴c² ⋅ a⁴c³

​

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

​

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SECOND: Simplify the expanded form.​

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EXAMPLE

Simplify: -5a³b⁴ ⋅ -9ab⁴

​

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

​

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SECOND: Simplify the expanded form.​

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