Surds and Exponents
Square and Square Root
√𝑎 × √𝑎 = (√𝑎 )2 = √𝑎2 = 𝑎
Product of Surds
√𝑎 × √𝑏 = √𝑎𝑏
Division of Surds
√𝑎
√𝑏
Denominator Rationalisation
- Square and Square Root
- Difference of Squares
Exponent / Power / Index
Negative and Reciprocal Exponent /
Power / Index
Fractional Exponent / Power / Index
Multiple of Same Base
Exponent Addition
Division of Same Base
Exponent Subtraction
Power to a Power
Exponent Multiplication
Power to a Fractional Power
Exponent Division
Power of a Product
= Product of the Powers
Power of a Quotient = Quotient of the
Powers
𝑏
√𝑎
=
𝑏
√𝑎
×
√𝑎
√𝑎
;
𝑎
𝑏
=√
𝑐
𝑎 + √𝑏
=
𝑐
𝑎 + √𝑏
×
𝑎 − √𝑏
𝑎 − √𝑏
𝑎𝑛 = 𝑎 × 𝑎 × ⋯ × 𝑎 } 𝑛 𝑓𝑎𝑐𝑡𝑜𝑟𝑠 𝑜𝑓 𝑎;
𝑎−𝑛 =
1
1 1
1
1
= × × ⋯ × } 𝑛 𝑓𝑎𝑐𝑡𝑜𝑟𝑠 𝑜𝑓 ;
𝑛
𝑎
𝑎 𝑎
𝑎
𝑎
1
𝑎𝑛 = 𝑛√𝑎
𝑎𝑚 × 𝑎𝑛 = 𝑎𝑚+𝑛
𝑎𝑚 ÷ 𝑎𝑛 =
𝑎𝑚
= 𝑎𝑚−𝑛
𝑎𝑛
(𝑎𝑚 )𝑛 = 𝑎𝑚𝑛
1
𝑛
𝑚
(𝑎𝑚 )𝑛 = √𝑎𝑚 = 𝑎 𝑛
(𝑎𝑏)𝑛 = 𝑎𝑛 𝑏𝑛
𝑎
𝑎𝑛
( )𝑛 = 𝑛
𝑏
𝑏
𝑎0 = 1
𝑎𝑛 =
1
𝑎−𝑛
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5