Exponents And Powers

 

• Numbers with exponents obey the following laws of exponents.
  (a) 
  (b)
  (c) 
  (d) 
  (e) 
  (f)
• Very small numbers can be expressed in standard form using negative exponents.
• Use of Exponents to Express Small Number in Standard form:
  (i)  Very large and very small numbers can be expressed in standard form.
  (ii)  Standard form is also called scientific notation form.
  (iii)  A number written as is said to be in standard form if m is a decimal number such that and n is either a positive or a negative integer.
• Examples: 150,000,000,000 = 1.5 x 1011.
• Exponential notation is a powerful way to express repeated multiplication of the same number. For any non-zero rational number ‘a’ and a natural number n, the product a x a x a x ........... x a(n times) = an.
  It is known as the nth power of ‘a’ and is read as ‘a’ raised to the power n’. The rational number a is called the base and n is called exponent.