Rules of exponents

Rules of exponents

1. 6.1 "Rules of exponents"

   • Product Rule: a⌃m  a⌃n = a⌃m+n
     • Example: x⌃2  x⌃3 = x⌃2+3
   • Quotient Rule: a⌃m/a⌃n = a⌃m−n
     • Example: y⌃2/y = y⌃2−1
   • Negative Exponent Rule: a⌃−m = 1/a⌃m
     • Example: y⌃−3 = 1/y⌃3
   • Zero Exponent Rule: a⌃0 = 1
     • Example: x⌃0 = 1
   • Raising a Power to a Power: (a⌃m)⌃n = a⌃mn
     • Example: (x⌃2)⌃6 = x⌃2  6 = x⌃12
   • Raising a Product to a Power: (ab)⌃m = a⌃m b⌃m
     • Example: (yx)⌃4 = y⌃4 x⌃4
   • Raising a Quotient to a Power: (a/b)⌃m = a⌃m/b⌃m
     • Example: (x/y)⌃2 = x⌃2/y⌃2

2. 6.2 "Rational Exponents"

   • Exponential Form of m√a is: n√a = a⌃1/n
     • Example: 3√x⌃11 = x⌃11/3
   • Exponential Form of n√a⌃m is: n√a⌃m = (n√a)⌃m = a⌃m/n
     • Example: 4√8⌃7 x⌃21 y⌃14 = (4√8x⌃3 y⌃2)⌃7 = (8x⌃3 y⌃2)⌃7/4

3. 6.3 "Simplifying radicals"

   • Product Rule for Radicals:n√a  n√b = n√ab
     • Example: √2  √5 = √10
   • Quotient Rule for Radicals: n√a/n√b = n√a/b
     • Example: √18/√3 = √18/3 = √6

4. Usefull knowledges: here; "" is a multiplying sign.