Laws of Exponents

You can demonstrate the laws of exponents with either Simplify or Combine + Powers. You can also use Combine + Exponential for the first of these equations. These laws work for real or complex exponents and for other expressions as well.

Simplify (or Combine + Powers)

2^x2^y =  2^x+y                

3^x = 3^xy                

= a^x-y

Scientific Notebook normally returns exponential expressions in the form  e^f(x) rather than exp f (x). However, when the exponent f (x) is sufficiently complicated, the linear form exp f (x) is returned. The following example illustrates these two behaviors.

Simplify (or Combine + Powers)

e^a+b =  e^{3a + bc}

e^x2-3xye^2x+5 =  expx² - 3xy + 2x + 5