Math for Life - Life: The Science of Biology, Seventh ... - WH Freeman

Math for LifeTOPIC 2: EXPONENTS AND POWERS OF TEN / Page 2This is a very useful shortcut if you are doing computations with powers of 10.EXPONENTS 2.2: Multiplying Numbers that Have ExponentsTo multiply two numbers with the same base, add the exponents.f s × f t = f s + tHere f is called the base. The two numbers f s and f t have the same base. So the exponentss and t can be added.EXAMPLE: 12 4 × 12 5 = 12 9WHY: (12 × 12 × 12 × 12) × (12 × 12 × 12 × 12 × 12) = 12 9The base, 12, is the same throughout, so we can just add the exponents 4 + 5 = 9. Theanswer is 12 9 .EXPONENTS 2.3: Raising Exponents to a PowerTo raise an expression that contains a power to a power, multiply the exponents.(j v ) w = j v × wThe exponents v and w are multiplied.EXAMPLE: (3 2 ) 3 = 3 6WHY: (3 × 3) × (3 × 3) × (3 × 3) = 3 6EXPONENTS 2.4: Dividing Numbers that Have ExponentsTo divide two numbers that have the same base, subtract the exponents.aamnm= a −anBACKTOCNEXT