Page 28 - Arithmetic

Square Root, Cube Root and Exponents Exponents
Exponent of ‘a’ is the number of times ‘a’ is multiplied by itself.
For example
a5 = a × a × a × a × a
where ‘a’ is the base and ‘5’ is the power. Here, ‘a’ is raised to the fifth power.
REMEMBER:
• A number raised to power zero is 1. 80 = 1
• A number raised to the power 1 is the number itself. 81 = 8 or x1 = x
• A number with a negative power is the reciprocal of the number. 8-1 = 1 or x-a = 𝟏 8 𝒙𝒂
• When multiplying two exponents, add the powers. 42 × 41 = 43 or (xa) (xb) = x(a + b)
• (xa)b = xab For example, (22)4 = 28
• When dividing two exponents, subtract the powers. 43 ÷ 42 = 41 or 𝐱𝐚 = x(a - b) 𝐱𝐛
• Exponent value of a negative number is negative when the power is odd.(- 4)3 = -64
• Exponent value of a negative number is positive when the power is even. (- 4)2 =16
Squares
The multiplication of a number by itself is known as the squaring of the number. The result is the square of the number.
In short, the numbers are raised to the second power.
For example, 52 = 25
Cubes
Square root
A square root of a number is some number which when multiplied by itself gives the original
2 number. The symbol used to denote a square root is √ or √.
For example, √36 = 6 because when 6 is multiplied by itself (6) it results in the original number (36).
When numbers are raised to the third power, the result is a cube of that number.
For example,
53 = 125
Page 27 of 55
Arithmetic Concept