**Important Concepts and Formulas Powers and 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

^{2}, the base is 5 and the exponent is 2.
2. 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 is
product form of 128 with base 2.

3. 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
4. (–1)

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

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

^{b}, where 1 ≤ a < 10 and b is an integer.