To know more about Exponents and powers Done By; krishnakousthubha

1. Welcome

2. Contents
1) What are exponents,
powers and bases?
2) Exponential notation
3) Laws of exponents
4) Standard form

3. Exponents, powers and bases
The base number tells what number is being
multiplied. The exponent, a small number
written above and to the right of the base
number, tells how many times the base
number is being multiplied.
For example, “6 to the 5th power” may be
written as “65.” Here, the base number is 6 and
the exponent is 5. This means that 6 is being
multiplied by itself 5 times: 6 x 6 x 6 x 6 x 6

4. Exponents, powers and bases

5. Exponential notation
A symbolic way of showing how many times a
number or variable is used as a factor.
In the notation 5
^3, the exponent 3
shows that 5 is a
factor used three
times; that is 5 ^3 =
5 x 5 x 5 =125.

6. Laws of exponents
Law 1: xmxn = xm+n Product law
Example: x2x3 = (xx)(xxx) = xxxxx = x5
So, x2x3 = x(2+3) = x5
Law 2: xm/xn = xm-n Quotient law
Example: x4/x2 = (xxxx) / (xx) = xx = x2
So, x4/x2 = x(4-2) = x2

7. Laws of exponents
Law 3: (xm)n = xmn Power law
Example: (x3)4 = (xxx)4 = (xxx)(xxx)(xxx)(xxx)
= xxxxxxxxxxxx = x12
So (x3)4 = x3×4 = x12
Law 4: xnyn=(xy)n
Example: x3y3 = (xxx)(yyy) = xxxyyy = xyxyxy
= (xy)(xy)(xy) = (xy)3

8. Laws of exponents
Law 5: (x/y)n = xn/yn
Example: (x/y)3 = (x/y)(x/y)(x/y) = (xxx)/(yyy) =
x3/y3
Law 6: x0 = 1
Example: 70 = 1
Law 7: x-n = 1/xn
Example: x-3 = 1/x3

9. Laws of exponents

10. Standard form
Standard form is a way of
expressing a number with one
whole number and the remaining
part as exponent of 10
Example: 10000000=1*107

11. Standard form
Expressing very large numbers in
standard form:
The formula is K*10n where 0<K<10
and n belongs to I
Example : 20000000 can be written as 2*107

12. Standard form
Expressing very small numbers in
standard form:
The formula is K*10-n where
0<K<10 and n belongs to I
Example: 0.000003 can be written as 3*10-6