why is 5 to the power of 0 one?

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$${{\mathtt{5}}}^{{\mathtt{0}}}$$why is 5 to the power of 0 one?

Guest Apr 25, 2014

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Best Answer

consider this

$$\frac{5}{5}=1\\\\
\frac{5^3}{5^3}=1\\\\
\mbox{but}\\\\
\frac{5^3}{5^3}=5^{3-3} = 5^0\\\\
\mbox{ therefore}\\\\
5^0=1$$

Melody Apr 25, 2014

Melody · Answer 1 · 2014-04-25T01:19:21

consider this

$$\frac{5}{5}=1\\\\
\frac{5^3}{5^3}=1\\\\
\mbox{but}\\\\
\frac{5^3}{5^3}=5^{3-3} = 5^0\\\\
\mbox{ therefore}\\\\
5^0=1$$

CPhill · Answer 2 · 2014-04-25T01:39:41

Re: why is 5 to the power of 0 one?

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In general, any real number raised to the "0" power is = 1

The only exception is 0⁰.........this is known as an "indeterminate" form - we can't define what this might be!!!

(It also involves division by 0......that's a no-no!!)