Introduction to Fractional powers in math:
In math, when the power or exponent is a fraction number then the number said to be having the functional powers in math. The example for the fractional power is `2^ (2/3)`
Rules:
Rules for the various operations on fractional powers in math.
For multiplication:
`m^ (a/b)` *`m^ (c/d)` = `m^ ((a/b) + (c/d))`
For division:
`m^ (a/b)` /`m^(c/d)` =` m^((a/b)-(c/d))`
`(m^ (a/b))^c` = `(m^(c/b))^a`
Model Problems for Multiplication of Fractional Power in Math:
Q 1: Find the value of the fractional power terms?
` 2^ (1/2)` * `2 ^ (3/2)`
Solution:
When we multiply the two terms with fractional powers. we need the fractional powers.
The rule is
`m^ (a/b)` *`m^ (c/d)` = `m^ ((a/b) + (c/d))`
here,
` 2^ (1/2)` * `2 ^ (3/2)` = `2 ^(1/2+3/2).`
= `2^((1+3)/2)`
= `2^(4/2)`
= `2^2`
= 4
Q 2 : Find the value of the fractional power terms?
` 2^ (5/2)` * `2 ^ (3/2)`
Solution:
When we multiply the two terms with fractional powers.we need to add the fractional powers.
The rule is
` m^ (a/b)` *`m^ (c/d)` = `m^ ((a/b) + (c/d))`
here
`2^ (1/2)` * `2 ^ (3/2)` =` 2 ^(5/2+3/2).`
= `2^((5+3)/2)`
= `2^(8/2)`
= `2^4`
= 16
Answer is 16.
Model Problems for Division of Fractional Power in Math:
Q 1: Find the value of the fractional power terms?
`2^ (5/2)` / `2 ^ (3/2)`
Solution:
When we divide the two terms with fractional powers. we need to subtract the fractional powers
The rule is
`m^ (a/b)` /`m^ (c/d) ` = `m^ ((a/b) - (c/d))`
here
`2^ (1/2)` / `2 ^ (3/2)` = `2 ^(5/2-3/2)` .
= `2^((5-3)/2)`
= `2^(2/2)`
= `2^1`
= 2
Answer is 2
Q 2 : Find the value of the fractional power terms?
`2^ (5/2)` / `2 ^ (3/4)`
Solution :
When we multiply the two terms with fractional powers. we need to subtract the fractional powers
The rule is
`m^ (a/b)` /`m^ (c/d)` = `m^ ((a/b) - (c/d))`
here
`2^ (1/2)` / `2 ^ (3/2)` = `2 ^(5/2-3/4).`
= `2^((10-3)/4)`
= `2^(7/4)`
Answer : 274
Q 3 : Find the value of the `(5^ (4/5)) ^10.`
Solution:
To find the value we use
` (m^ (a/b))^c` = `(m^(c/b))^a`
`(5^ (4/5)) ^10 ` = `(5^ (10/5)) ^4.`
= `(5^ (2)) ^10.`
= `5^ (2*10)`
= `5^20`
Answer is `5^20`
In math, when the power or exponent is a fraction number then the number said to be having the functional powers in math. The example for the fractional power is `2^ (2/3)`
Rules:
Rules for the various operations on fractional powers in math.
For multiplication:
`m^ (a/b)` *`m^ (c/d)` = `m^ ((a/b) + (c/d))`
For division:
`m^ (a/b)` /`m^(c/d)` =` m^((a/b)-(c/d))`
`(m^ (a/b))^c` = `(m^(c/b))^a`
Model Problems for Multiplication of Fractional Power in Math:
Q 1: Find the value of the fractional power terms?
` 2^ (1/2)` * `2 ^ (3/2)`
Solution:
When we multiply the two terms with fractional powers. we need the fractional powers.
The rule is
`m^ (a/b)` *`m^ (c/d)` = `m^ ((a/b) + (c/d))`
here,
` 2^ (1/2)` * `2 ^ (3/2)` = `2 ^(1/2+3/2).`
= `2^((1+3)/2)`
= `2^(4/2)`
= `2^2`
= 4
Q 2 : Find the value of the fractional power terms?
` 2^ (5/2)` * `2 ^ (3/2)`
Solution:
When we multiply the two terms with fractional powers.we need to add the fractional powers.
The rule is
` m^ (a/b)` *`m^ (c/d)` = `m^ ((a/b) + (c/d))`
here
`2^ (1/2)` * `2 ^ (3/2)` =` 2 ^(5/2+3/2).`
= `2^((5+3)/2)`
= `2^(8/2)`
= `2^4`
= 16
Answer is 16.
Model Problems for Division of Fractional Power in Math:
Q 1: Find the value of the fractional power terms?
`2^ (5/2)` / `2 ^ (3/2)`
Solution:
When we divide the two terms with fractional powers. we need to subtract the fractional powers
The rule is
`m^ (a/b)` /`m^ (c/d) ` = `m^ ((a/b) - (c/d))`
here
`2^ (1/2)` / `2 ^ (3/2)` = `2 ^(5/2-3/2)` .
= `2^((5-3)/2)`
= `2^(2/2)`
= `2^1`
= 2
Answer is 2
Q 2 : Find the value of the fractional power terms?
`2^ (5/2)` / `2 ^ (3/4)`
Solution :
When we multiply the two terms with fractional powers. we need to subtract the fractional powers
The rule is
`m^ (a/b)` /`m^ (c/d)` = `m^ ((a/b) - (c/d))`
here
`2^ (1/2)` / `2 ^ (3/2)` = `2 ^(5/2-3/4).`
= `2^((10-3)/4)`
= `2^(7/4)`
Answer : 274
Q 3 : Find the value of the `(5^ (4/5)) ^10.`
Solution:
To find the value we use
` (m^ (a/b))^c` = `(m^(c/b))^a`
`(5^ (4/5)) ^10 ` = `(5^ (10/5)) ^4.`
= `(5^ (2)) ^10.`
= `5^ (2*10)`
= `5^20`
Answer is `5^20`
