**Important Concepts and Formulas on Exponents**

1. The exponential form of a given
number is a way of expressing it using a base and a raised number called
exponent. For example, in 5

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^{2}, the base is 5 and the exponent is 2.To see solved examples on exponents ------- Click Here!

2. 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 is
product form of 128 with base 2.

3. When base is positive, the result
will be positive.

4. When base is negative and power is an
odd number, the result will be negative.

5. When base is negative and power is an
even number, the result will be positive.

6. When 1 is raised to any power, the
result will be equal to 1.

7. We denote the reciprocal of a number
a by a

^{–1}, i.e. a^{–1}= 1/a . Hence, the reciprocal of (p/q)^{m}is (q/p)^{m}.
8. The following are the laws of
exponents for a and b which are non-zero integers and m and n are whole
numbers.

·
a

^{m}× a^{n}= a^{m + n}
·
a

^{m}÷ a^{n}= a^{m – n}, when m > n
·
(a

^{m})^{n}= a^{mn}
·
a

^{m}× b^{m}= (ab)^{m}
·
a

^{m}÷ b^{m}= (a/b)^{m}
·
a

^{0}= 1
9. (–1)

^{even number}= 1 and (–1)^{odd number}= –1
10. Standard form is a way of writing
very large numbers or very small numbers in short form.

11. The standard form of a number is a ×
10

^{b}, where 1 ≤ a < 10 and b is an integer. For example, 61,20,000 can be written as 6.12 × 10^{6}.