Rules with Exponents

​base

​exponent

​2³ means 2 x 2 x 2 which equals 8

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 ​

​ZERO RULE

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Any BASE to the power of 0 simply equals ONE.

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Example: 4⁰ =

Example: z⁰=

EXAMPLES

a² ⋅ a⁵ = a ⋅ a ⋅ a ⋅ a ⋅ a ⋅ a ⋅ a = a⁷

​

SHORTCUT: just ADD the EXPONENTS

​y⁶ ⋅ y⁷ =​

EXAMPLE

​z⁵y³x^-2 ⋅ z⁶y⁵x⁷ = z⁵ ⋅ y³ ⋅​ x^-2 ⋅​ z⁶ ⋅ y⁵ ⋅​ x⁷

EXAMPLE

​4x³ ⋅ 5x² = 4 ⋅ x³ ⋅ 5 ⋅ x²

​Multiplication is commutative, so we can rearrange them.

EXAMPLES

(a³)² = (a ⋅ a ⋅ a)² = a ⋅ a ⋅ a ⋅ a ⋅ a ⋅ a = a⁶

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​​SHORTCUT: just MULTIPLY the EXPONENTS

(w⁷)⁴​ =

​

​(a³b⁶c^-2)² = a^3⋅2 ⋅ b^6⋅2⋅ c^-2⋅2

​(4x³y⁴)² = (4¹x³y⁴)²

​(a³b⁶c^-2)⁰ =

​(3x⁰y^-5)³ =

EXAMPLE​​

EXAMPLES​​

EXAMPLE​​

EXAMPLE​​

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STEP 1: Flip the expression and change the exponent to positive

STEP 2: Apply the positive exponent

STEP 1: Flip the expression and change the exponent to positive

STEP 2: Apply the positive exponent