Mathematics module 6

Mathematics module 6

1. 6.1: Rules of exponents

   • Product rule:
     • A m*A n=A m+n
       • 2 3* 2 2=2 5
   • Quotient rule:
     • A m/A n=A m-n
       • 3 7/ 3 5= 3 2
   • Negative exponent rule:
     • A-m= 1/ A m
       • 7 -2= 1/7 -2
   • Zero exponent rule:
     • A 0= 1
       • 15 0= 1
   • Raising a power to power:
     • (A m) n= A m*n
       • (2 3) 2= 2 6
   • Raising a product to a power:
     • (AB) m = A m B m
       • (5*6) 2= 5,2 6,2
   • Raising a quotient to a power:
     • (A/B)m=Am/Bm
       • (4/7)2= 4 2/ 7 2

2. 6.2: Rational exponents

   • m¬x n=(x) n/m
     • ¬x 5= (x)5/2

3. 6.3: Simplifying radicals

   • Product rule for radicals:
     • n¬A* n¬B= n¬AB
       • ¬2*¬5=¬10
   • Quotient rule for radicals:
     • n¬A/n¬9=n¬A/B
       • ¬18/¬3=¬18/3=¬6

4. 6.4: Addition and substration of radicals:

   • Simplify and combine radicals.
     • 5¬x8=x3¬x3