**Why is ***a*^{0 }= 1?

*a*

^{0 }= 1?

*2*

^{2}=4).

**So I start with 3!**

^{5}=

**243**

^{ }3

^{4 }=

**81**

^{ }3

^{3 }=

**27**

^{ }3

^{2 }=

**9**

^{ }3

^{1 }=

**3**

^{0 }=

**1**

**Notice that when we divide the answers by the base (3) it gives us the following answers.**

**243**/3 = 81

**81**/3 = 27

**27**/3 = 9

**9**/3 = 3

**3**/3 = 1

**If need be you can now use different bases to show the pattern always works.**

**Patterns with Negative Bases**

**You can now continue the pattern by showing them negative bases.**

^{5}=

**-243**

^{4 }=

**81**

^{3 }=

**-27**

^{2 }=

**9**

^{1 }=

**-3**

^{0 }=

**1**

**Notice that when we divide the answers by the base (-3) it gives us the following answers.**

**-243)**/(-3) = 81

**81**/(-3) = -27

**-27**)/(-3) = 9

**9**/(-3) = -3

**-3**)/(-3) = 1

**Patterns with Negative Exponents**

**This patter continues on for negative exponents as well.**

3 ^{3} = 273 ^{2} = 93 ^{1} = 33 ^{0} = 13 ^{−1}= 1/3 3 ^{−2} = 1/93 ^{−3} = 1/273 ^{−4} = 1/81 |

**So...**

**Finally, Make sure to point out that...**

^{1}

**= 1/3**

^{2}

^{3}

^{4}

^{5}

**Now you're ready to move on to Exponents that are Fractions!**

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