In this video I go over a simple proof of the general law of exponent with base a: a^x+y = a^xa^y. In the proof I use the definition a^x = e^{x ln a} and the laws of exponents with base e which I covered in my earlier videos

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Laws of Exponents – a^x+y = a^xa^y

General Laws of Exponents

If x and y are real numbers and a > 0, then:

1. a^x+y = a^xa^y
2. a^x-y = a^x/a^y
3. (a^x)^y = a^xy
4. (ab)^x = a^xb^x

Recall from my previous videos:

1. e^x+y = e^xe^y
2. e^x-y = e^x/e^y
3. (e^x)^r = e^rx

Also Recall Definition: a^x = e^{x lna}

Proof: