Why is 5 to the 0 power always 1? Can you give me an explanation please?

Crystal

Education level: Middle School/Junior High

Hi Crystal,

The use of exponential notation is a great, laboursaving device. It is much easier to write 5⁸ than 5  5  5  5  5  5  5  5. This notation also simplifies some manipulations

5⁸ 5¹¹ = 5^{8 + 11} = 5¹⁹

To multiply two powers with the same base you just add the exponents. If you then agree with the use of negative exponents, for example that 5^-9 = ¹/_5⁹ then you can perform calculations like

5¹⁹ 5^-9 = 5¹⁰

Again you just add the exponents.

But what about 5⁹ 5^-9? I know this means 5⁹ divided by 5⁹ which is 1, but if I add the exponents I get 5⁰. So if you want the statement To multiply two powers with the same base you just add the exponents to remain true for positive and negative exponents you must have 5⁰ = 1.

Penny

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