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# Exponents

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why does 3 to the power of 0 always 1

Guest May 25, 2017

#1
+1224
+2

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

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

$$3^{10}$$ 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, $$x^0=1\hspace{1cm},x\neq0$$

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

$$3^{10}$$ 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

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