Introduction to Standard Exponential Form
Notation : `a^b` , where a is known as base and b is known as exponent which must be a positive and integral value. I like to share this Exponential Function Definition with you all through my article.
Explanation of `a^b` : The standard exponential form, `a^b` can mathematically be expressed as `a` multiplied by itself `b` times. That is to say
`axxaxxaxxaxx.... b "times"`. This yeilds a single number if we know the value of a and b.
eg. Assuming a = 2 and b = 3 , we can express `a^b` = `2^3` = `2xx2xx2` = 8(as b = 3 so we multiply a = 2 with itself 3 times). Note that the answer 8 results in single number.
Sample Examples of the Exponential Form:
1. `3^2` = `3xx3` = `9` (3 multiplied by itself 2 times)
2. `4^3` = `4xx4xx4` = `64` (4 multiplied by itself 3 times)
[Note: Here in standard exponential form, if we assume a and/or b are variables, they do not yeild any number. Instead they remain in the variable format. like
3. `x^3` = `x xx x xx x` (`x` multiplied by itself 3 times)
4. `x^a` = `x xx x xx x xx ... ` (`x` multiplied by itself a times) ]
[ Notes 2. If we take `b` as a decimal value such as 0.3, it comes under the section of nth root of a number, while here we are discussing how to compute standard exponential form ]
Abstracts of Standard Exponential Form:
Following are the rules and abstracts to calculate expressions involvint standard exponential forms.
1. `(a^b)^c` = `a^(bc)`
eg. a. `(2^3)^2` = `2^(3xx2)` = `2^6` = `2xx2xx2xx2xx2xx2` = 64
b. `(3^2)^4` = `3^(2xx4)` = `3^8` = `3times3times3times3times3times3times3times3`
Abstracts of Standard Exponential Form (continued)
2. `a^b xx a^c` = `a^(b+c)` (constraints : Both exponential form must have base that are equal)
`a^b//a^d` = `a^(b-d)` ( For multiplication, both exponents are added, while for division, exponent for numerator is subtracted by exponent of denominator.Please express your views of this topic 7th grade math problems online by commenting on blog.
Examples :
1. `5^2xx5^3` = `5^(2+3)`= `5^5` = 3125
2. `3^5//3^2` = `3^(5-2)` = `3^3` = 27
3. `a^(-c) = 1/a^c` (when exponent is a negative number, one can make it positive by reciprocating the expression.)
such as `2^-3` = `1/2^3` = `1/8`
Example Problems on Standard Exponential Form
Can you compute these expressions
`3^5 = `
`x^3=`
`x^b=`
`(2^2)^4 = `
`2^5 xx 2^3 = `
`2^8//2^5 =`
`2^-3 = "(convert to positive exponential form)"`
Compute `(2^5xx2^7)/2^4`
Notation : `a^b` , where a is known as base and b is known as exponent which must be a positive and integral value. I like to share this Exponential Function Definition with you all through my article.
Explanation of `a^b` : The standard exponential form, `a^b` can mathematically be expressed as `a` multiplied by itself `b` times. That is to say
`axxaxxaxxaxx.... b "times"`. This yeilds a single number if we know the value of a and b.
eg. Assuming a = 2 and b = 3 , we can express `a^b` = `2^3` = `2xx2xx2` = 8(as b = 3 so we multiply a = 2 with itself 3 times). Note that the answer 8 results in single number.
Sample Examples of the Exponential Form:
1. `3^2` = `3xx3` = `9` (3 multiplied by itself 2 times)
2. `4^3` = `4xx4xx4` = `64` (4 multiplied by itself 3 times)
[Note: Here in standard exponential form, if we assume a and/or b are variables, they do not yeild any number. Instead they remain in the variable format. like
3. `x^3` = `x xx x xx x` (`x` multiplied by itself 3 times)
4. `x^a` = `x xx x xx x xx ... ` (`x` multiplied by itself a times) ]
[ Notes 2. If we take `b` as a decimal value such as 0.3, it comes under the section of nth root of a number, while here we are discussing how to compute standard exponential form ]
Abstracts of Standard Exponential Form:
Following are the rules and abstracts to calculate expressions involvint standard exponential forms.
1. `(a^b)^c` = `a^(bc)`
eg. a. `(2^3)^2` = `2^(3xx2)` = `2^6` = `2xx2xx2xx2xx2xx2` = 64
b. `(3^2)^4` = `3^(2xx4)` = `3^8` = `3times3times3times3times3times3times3times3`
Abstracts of Standard Exponential Form (continued)
2. `a^b xx a^c` = `a^(b+c)` (constraints : Both exponential form must have base that are equal)
Examples :
1. `5^2xx5^3` = `5^(2+3)`= `5^5` = 3125
2. `3^5//3^2` = `3^(5-2)` = `3^3` = 27
3. `a^(-c) = 1/a^c` (when exponent is a negative number, one can make it positive by reciprocating the expression.)
such as `2^-3` = `1/2^3` = `1/8`
Example Problems on Standard Exponential Form
Can you compute these expressions
`3^5 = `
`x^3=`
`x^b=`
`(2^2)^4 = `
`2^5 xx 2^3 = `
`2^8//2^5 =`
`2^-3 = "(convert to positive exponential form)"`
Compute `(2^5xx2^7)/2^4`
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