Numbers with negative exponents follow these laws:
am x an = am+n
am an = am-n , m > n
(am)n = amn
am x bm = (ab)m
am bm = (a/b)m
a0 = 1
Very small numbers can be expressed in standard form using negative exponents.
Use of Exponents to Express Small Number in Standard form:
Very large and very small numbers can be expressed in standard form.
Standard form is also called scientific notation form.
A number written as m x 10n is said to be in standard form if m is a decimal number such that 1≤ m < 10 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 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.