+0

# Exponents

0
113
1

why does 3 to the power of 0 always 1

Guest May 25, 2017

#1
+1224
+2

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

$$3^{10}$$ 3*3*3*3*3*3*3*3*3*3 $$59049$$ 3*3*3*3*3*3*3*3*3 $$19683$$ 3*3*3*3*3*3*3*3 $$6561$$ 3*3*3*3*3*3*3 $$2187$$ 3*3*3*3*3*3 $$729$$ 3*3*3*3*3 $$243$$ 3*3*3*3 $$81$$ 3*3*3 $$27$$ 3*3 $$9$$ 3 $$3$$ ? ?

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
Sort:

#1
+1224
+2

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

$$3^{10}$$ 3*3*3*3*3*3*3*3*3*3 $$59049$$ 3*3*3*3*3*3*3*3*3 $$19683$$ 3*3*3*3*3*3*3*3 $$6561$$ 3*3*3*3*3*3*3 $$2187$$ 3*3*3*3*3*3 $$729$$ 3*3*3*3*3 $$243$$ 3*3*3*3 $$81$$ 3*3*3 $$27$$ 3*3 $$9$$ 3 $$3$$ ? ?

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

### 9 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details