rules of exponents module 6

rules of exponents module 6

1. Lesson 6.1

   • raising a product to a power
     • general formula〖(ab)〗^6=a^6 b^6
       • example (abc)^9=a^9 b^9 c^9
   • raising a quotient to a power
     • general formula (a/b)^m=a^m/b^m
       • example (8/2)^3=8^3/2^3
   • zero exponent rule
     • general formula a^0=1
       • example 160^0=1
   • negative exponent rule
     • general formula a^(-m)=1/a^m
       • example 〖17〗^(-7)=1/〖17〗^7
   • Quotient rule
     • general formula a^m/a^n =a^(m-n)
       • example 〖10〗^5/2^3 =5^2
   • Product rule
     • general formula a^m*a^n=a^(m+n)
       • example 5^3*4^2=〖20〗^5
   • raising a power to a power
     • general formula ( a^m)^n=a^mn
       • example (〖12〗^5)^7=〖12〗^35

2. Lesson 6.2

   • exponential form of √(n&a)
     • general formula √(n&a)=a^(1/n)
       • example √(2&7)=7^(1/2)
   • exponential form of √(n&a^m )
     • general formula √(n&a^m )=a^(m/n)
       • example √(5&2^7 )=2^(7/5)
   • exponential form of √(n&a^n )
     • general formula √(n&a^n )=a
       • example √(2&9^2 )=9^

3. lesson 6.3

   • general formula √(n&a)*√(n&b)=√(n&ab)
     • example √(2&2)*√(2&5)=√(2&10)
     • product radical for radicals
   • quotient rule for radicals
     • general formula √(n&a)/√(n&b)=√(n&a/b)
       • example √(2&18)/√(2&3)=√(2&18/3)