Maths- Indices Flashcards
Rules of indices
You can perform operations on numbers that have been squared cubed or raised to higher powers. There are three rules to remember for multiplying, dividing, and the power of a power.
Multiplying
When multiplying add the powers.
23 × 24 = (2 × 2 × 2) × (2 × 2 × 2 × 2)
= 27
Dividing
When dividing subtract the powers.
25 ÷ 22 = = 2 × 2 × 2 (Cancelling two of the 2s)
= 23
The power of a power
When taking the power of a number already raised to a power, multiply the powers.
For example this is how to find the square of 23.
square of 23 = (23)2 = (2 × 2 × 2) × (2 × 2 × 2) = 26
Notice that the answer has an index of 6, which comes from multiplying the powers at the beginning (3 x 2). Here is another example.
(22)4 = (2 × 2) × (2 × 2) x (2 × 2) × (2 × 2) = 28
So you see that in both examples the powers have been multiplied (3x2 and 2x4)
Squaring a number
3^2 means ‘3 squared’, or 3 x 3.
The small 2 is an index number, or power. It tells us how many times we should multiply 3 by itself.
Similarly 72 means ‘7 squared’, or 7 x 7.
And 102 means ‘10 squared’, or 10 x 10.
So, 12 = 1 x 1 = 1
22 = 2 x 2 = 4
32 = 3 x 3 = 9
42 = 4 x 4 = 16
52 = 5 x 5 = 25
etc
1, 4, 9, 16, 25… are known as square numbers.
Square roots
The opposite of a square number is a square root.
We use the symbol to mean square root.
So we can say that = 2 and = 5.
However, this is not the whole story, because -2 x -2 is also 4, and -5 x -5 is also 25.
So, in fact, = 2 or -2. And = 5 or -5.
Remember that every positive number has two square roots.
Cubing a number
2 x 2 x 2 means '2 cubed', and is written as 2^3. 1^3 = 1 x 1 x 1 = 1 2^3 = 2 x 2 x 2 = 8 3^3 = 3 x 3 x 3 = 27 4^3 = 4 x 4 x 4 = 64 5^3 = 5 x 5 x 5 = 125 etc 1, 8, 27, 64, 125… are known as cube numbers.
Cube roots
e opposite of a cube number is a cube root. We use the symbol to mean cube root.
So is 2 and is 3.
Each number only has one cube root.
