Quandaries
and Queries 

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 5^{8} than 5 5 5 5 5 5 5 5. This notation also simplifies some manipulations
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
Again you just add the exponents. But what about 5^{9} 5^{9}? I know this means 5^{9} divided by 5^{9} which is 1, but if I add the exponents I get 5^{0}. 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 5^{0} = 1. Penny 

