subject: Powers Instead Of Exponentials [print this page] Exponential: Exponential:
The exponential function is one of the function represented as ex, where e- number nearly 2.718281828. Function ex similar to its own derivative.
Power instead of Exponential:
If a is some integer and n some non negative integer then the product of a with itself n times, a*a*.....*a, is known as raised to the power n, and it can be denoted as an.
powers
Example for Power Instead of Exponential:
The following examples defines the power function instead of exponential:
200=1
11=1
42= 4*4 =16
73= 7*7*7 = 343
55 = 5*5*5*5*5 = 3125
Rules for Power Instead of Exponential:
The following rules are used to compute the power series:
Power using addition: If the two numbers which is same alphabet or number are multiplied with power then the two powers are added.
pmx pm pn=pm+n
Power using subtraction: If the two numbers which is same alphabet or number are divided with power then the two powers are subtracted.
pm-: pn=pm-n
Power using multiplication: The following form is used to while we multiply tow power.
(pm)n=pmn
Power with one:
p1=p
Power with zero:The general form of any thing power 0 gives 1.
p0=1
Negative Power:
The following steps are used to defines the negative power instead of exponential:
Let, p^2-:p^5 = (p^2)/(p^5) =(pxxp)/(pxxpxxpxxpxxp)
By applying the second rule
Let, p^2-:p^5 =p^(2-5)=p^-3
Hence, p-3=1/p3.
The general form is, p-n=1/pn
Example:
2-5=1/25=32
3436=3(4-6)=3-2=1/32=1/9
Fractional Power:
If p is positive integer, then the square root of p is the integer that is multiplied by itself which defines p. Hence, 5 is a square root of 25 that is 52=25.
Now we can write this as 5=sqrt(25) .
Understand we can by the definition sqrt(p)xxsqrt(p)=p
The general idea for this is if p is a positive integer and n is a non negative integer then we can say,
p^(1/2)=root(n)(p)
Here, root(n)(p)- nth root of p.
The exponent says the number of times the base must be multiplied by it self, Exponent is the part of algebra and they have defined laws, with the help of it we can simplify the given exponent expressions.
