Numbers with exponents obey the following laws of exponents. 

Very small numbers can be expressed in standard form using negative exponents. (Scroll down to continue …)

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Use of Exponents to Express Small Number in Standard form:

1. Very large and very small numbers can be expressed in standard form.
2. Standard form is also called scientific notation form.

(iii) A number written as number such that is said to be in standard form if m is a decimal 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.