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why is any number to no power (for example: 197^0=1) always equal to 1

 Apr 26, 2014

Best Answer 

 #2
avatar+118667 
+5

Good answer anonymous!

I just want to go over what you were saying.

Anything divided by itself is 1

so

 $${\frac{{\mathtt{7}}}{{\mathtt{7}}}} = {\mathtt{1}}$$

$$\frac{9^3}{9^3}=1$$

also

 $$\frac{5^7}{5^4}=5^7\div 5^4=5^{7-4}=5^3$$

so

$$\frac{9^3}{9^3}=9^{3-3}=9^0$$   BUT we know that    $$\frac{9^3}{9^3}=1$$

therefore

$$9^0=1$$      

Anything (except for 0) raised to the power of 0 is 1.     

$${{\mathtt{0}}}^{{\mathtt{0}}} = \underset{{\tiny{\text{Error: indeterminante}}}}{{{\mathtt{0}}}^{{\mathtt{0}}}}$$    Like it says 00 is undefined    

 

Are you happy now bioschip? 

 Apr 27, 2014
 #1
avatar
+5

It just is but think of it like this

take 2 for example

2=2^1

and if we times 2 by 2  then it becomes  2^2

and again it becomes  2^3

this is ovious so when we multiply it by itself we add one on the power

so when we divide we take on off

2/2 = 2^0

and 2/2 = 1 and this is the same for every number

2^0 / 2 = 2^-1     and so on

hope this helps you understand

 Apr 26, 2014
 #2
avatar+118667 
+5
Best Answer

Good answer anonymous!

I just want to go over what you were saying.

Anything divided by itself is 1

so

 $${\frac{{\mathtt{7}}}{{\mathtt{7}}}} = {\mathtt{1}}$$

$$\frac{9^3}{9^3}=1$$

also

 $$\frac{5^7}{5^4}=5^7\div 5^4=5^{7-4}=5^3$$

so

$$\frac{9^3}{9^3}=9^{3-3}=9^0$$   BUT we know that    $$\frac{9^3}{9^3}=1$$

therefore

$$9^0=1$$      

Anything (except for 0) raised to the power of 0 is 1.     

$${{\mathtt{0}}}^{{\mathtt{0}}} = \underset{{\tiny{\text{Error: indeterminante}}}}{{{\mathtt{0}}}^{{\mathtt{0}}}}$$    Like it says 00 is undefined    

 

Are you happy now bioschip? 

Melody Apr 27, 2014

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