Aug 11, 2023 · How do I prove that these laws of exponents work for all real numbers NOT only just the positive integers ? for example (a.b)^n = a^n.b^n or any other law of exponents.

Dec 13, 2014 · How to prove exponent laws for various number systems, including real exponents Ask Question Asked 10 years, 11 months ago Modified 10 years, 11 months ago

Jan 27, 2016 · By abusing the laws of exponents for rational exponents, one can come up with any number of apparent paradoxes, in which a number seems to be shown as equal to its opposite …

I have managed to prove the usual exponent laws for integer exponents, using induction on the natural numbers. I am now trying to prove that the laws also hold for rational exponents. I'm startin...

Jan 25, 2016 · Think about square root on the complex plane. It can't be defined everywhere. If you try to define it everywhere continuity has to break somewhere. That's why you need branches of such …

Mar 16, 2018 · Rational ones are possible provided the denominator of the simplified fraction is odd --- Need to include the proviso that for rational exponents the evaluation process begins by writing the …

Jan 23, 2017 · I have read through this thread. It mentions that there a several conventions for rational exponents.The first condition for the first convention for exponent laws to apply is that the base be …

Jun 20, 2020 · I was working on a problem displaying the expansion of the definition of exponents, and naturally the final question was to prove the exponent laws when the exponents are real numbers.

Jun 8, 2020 · Exponent Laws [confused?] Ask Question Asked 5 years, 5 months ago Modified 5 years, 5 months ago

Feb 8, 2024 · Then use the fact that real numbers are the limits of rational numbers to prove it for all real numbers. You may find the exponent laws (Proposition 6.7.3) to be useful. (Proposition 6.7.3 states …