The term exponent says a number how many times to use and in a multiplication. Exponent is a operation and written as bⁿ, involving two numbers, the base b and the exponent or power n.
Here go to learn about these.
Exponent means write large numbers in a shorter form using exponents.
Like - 10, 000 = 10 x 10 x 10 x 10 = 104
The number 104 is read as 10 raised to the power of 4 or simply as fourth power of 10. 104 is called the exponential form of 10,000.
Similarly 102, which is 10 raised to the power 2, also read as ‘10 squared’ and 103, which is 10 raised to the power 3, also read as ‘10 cubed’.
Let's suppose a is any integer, than we can find the exponent like-
a x a = a2 (read as ‘a squared’ or ‘a raised to the power 2’)
a x a x a = a3 (read as ‘a cubed’ or ‘a raised to the power 3’)
a x a x a x a = a4 (read as a raised to the power 4 or the 4th power of a)
..............................
a x a x a x a x a x a x a = a7 (read as a raised to the power 7 or the 7th power of a) and so on.
As we know about the addition, subtraction, multiplications and division. The same operation can do with the exponents.
Multiplying Powers with the Same Base
Let us calculate 22 x 23 22 x 23 = (2 x 2) x (2 x 2 x 2)
= 2 x 2 x 2 x 2 x 2 = 25 = 22+3
We can generalise that for any non-zero integer a, where m and n are whole numbers, amx an= am + n
Dividing Powers with the Same Base
As like multiplications, the division has some rules for any non-zero integer a, am÷ an= am − n
where m and n are whole numbers and m > n.
For any non-zero integer ‘a’, where ‘m’ and ‘n’ are whole numbers, (am)n= amn
Multiplying Powers with the Same Exponents
In general, for any non-zero integer a amx bm= (ab)m(where m is any whole number)
Dividing Powers with the Same Exponents
Where a and b are any non-zero integers and m is a whole number.
Am/bm = am/bm = (a/b)m
Here we can Write exponential in many form that you seen.
You may also use (am)n= amn
Decimal Number System
In decimal we know that places of the 10th, 100th, 1000th etc and value in decimal of these.
Similarly we can expand the number with exponent and find the decimal values.
Let us look at the expansion of 47561, which we already know:
47561 = 4 x 10000 + 7 x 1000 + 5 x 100 + 6 x 10 + 1
Expressing Large Numbers in The Standard Form
We have expressed all these numbers in the standard form. Any number can be expressed as a decimal number between 1.0 and 10.0 including 1.0 multiplied by a power of 10. Such a form of a number is called its standard form.
The exponent of 10 in the standard form is 11 − 1 = 10. In 5985.3 there are 4 digits to the left of the decimal point and hence the exponent of 10 in the standard form is 4 − 1 = 3.