+0  
 
0
276
1
avatar

why does 3 to the power of 0 always 1

Guest May 25, 2017

Best Answer 

 #1
avatar+2117 
+2

As a generalization, \(x^0=1\hspace{1cm},x\neq0\)

 

This table may help you understand why 3^0=1

\(3^{10}\)   3*3*3*3*3*3*3*3*3*3 \(59049\)
\(3^9\)   3*3*3*3*3*3*3*3*3 \(19683\)
\(3^8\)   3*3*3*3*3*3*3*3 \(6561\)
\(3^7\)   3*3*3*3*3*3*3 \(2187\)
\(3^6\)   3*3*3*3*3*3 \(729\)
\(3^5\)   3*3*3*3*3 \(243\)
\(3^4\)   3*3*3*3 \(81\)
\(3^3\)   3*3*3 \(27\)
\(3^2\)   3*3 \(9\)
\(3^1\)   3 \(3\)
\(3^0\)   ? ?

 

Do you notice a pattern? I do. As you go down the list, you can divide by three to get to the next value. Therefore, if 3^1=3, all you have to do to get the next value is to divide by three. 3^1/3=1, so 3^0=1.

 

Here's another way of thinking about it. This method works for any number to the power of 0:

 

\(1=\frac{x^n}{x^n}=x^{n-n}=x^0\hspace{1cm},x\neq0\)

TheXSquaredFactor  May 25, 2017
 #1
avatar+2117 
+2
Best Answer

As a generalization, \(x^0=1\hspace{1cm},x\neq0\)

 

This table may help you understand why 3^0=1

\(3^{10}\)   3*3*3*3*3*3*3*3*3*3 \(59049\)
\(3^9\)   3*3*3*3*3*3*3*3*3 \(19683\)
\(3^8\)   3*3*3*3*3*3*3*3 \(6561\)
\(3^7\)   3*3*3*3*3*3*3 \(2187\)
\(3^6\)   3*3*3*3*3*3 \(729\)
\(3^5\)   3*3*3*3*3 \(243\)
\(3^4\)   3*3*3*3 \(81\)
\(3^3\)   3*3*3 \(27\)
\(3^2\)   3*3 \(9\)
\(3^1\)   3 \(3\)
\(3^0\)   ? ?

 

Do you notice a pattern? I do. As you go down the list, you can divide by three to get to the next value. Therefore, if 3^1=3, all you have to do to get the next value is to divide by three. 3^1/3=1, so 3^0=1.

 

Here's another way of thinking about it. This method works for any number to the power of 0:

 

\(1=\frac{x^n}{x^n}=x^{n-n}=x^0\hspace{1cm},x\neq0\)

TheXSquaredFactor  May 25, 2017

12 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.