What are exponents? When do we need them?
In simple words, exponents are the shorter way to write the repeated multiplication of a number.
Let’s clear the above sentence by doing the following example:
Consider we have the following repeated multiplication of ‘2s”
2 x 2 x 2
We can write it using exponents as shown below:
2 x 2 x 2 = 2³
The number which is repeated in multiplication becomes the “BASE” of and “number of times” it got repeated becomes the “EXPONENT” or “POWER” of the “BASE”.
2³ is read as “2 to the power 3” or “2 raised to the power of 3”
For practice: Learners can practice on to find out the base and exponent (power) in the following examples:
5³; 7³, 3² , 6², 4
Notes:
- In case of 4, we only see the base but no exponent. This got exponent “1” which means no repetition just by itself and which needs not to be shown. Hence all the real numbers have exponent “1” and which is understood in math.
- An exponent can be a whole number (0, 1, 2, 3, .......), a fraction (1/2, 1/3, 2/3 etc.) or even negative (......-3, -2, -1, -1/2)
- 5ᵒ = 1; This is a very good basic rule for exponents to remember. Any number with an exponent or power zero gives us “1” as the answer.
- There are special names for some special exponents. For example, power two is called square, power three is called cube and power ½ is called square root and power 1/3 is called cube root. For example; 3² is called three squared, 5² is called 5 squared and 5³ is called 5 cubed.
Importance:
Knowledge of exponents is the key for higher math. Kids in grade 6 and 7 should know all the above basics about exponents. In grade 8 and higher they should know the special rules for exponents. We need them to make math equation shorter as they are shorter way to write repeated multiplication and need exponents to develop logarithmic understanding which is a key to further higher studies in mathematics, physics and astronomy.