Question

Divide x to the 3 fifths power divided by x to the 1 fourth power.

Answer 1

`x^{(7)/(20)}`

Explanation:

`(x^(3)/(5) )/(x^(1)/(4) )`

To divide it we apply exponential property

`(a^m)/(a^n) =a^(m-n)`

when the base are same and the exponents are in division then we subtract the exponents

`(x^(3)/(5) )/(x^(1)/(4) )`

`x^{(3)/(5)-(1)/(4)}`

To subtract the fractions , the denominators should be same

LCD is 20

`x^{(3 \cdot 4)/(5 \cdot 4)-(1 \cdot 5)/(4 \cdot 5)}`

`x^{(12)/(20)-(5)/(20)}`

`x^{(7)/(20)}`

Answer 2

We can write the equation as
`(x^ (3)/(5) )/(x (1)/(4) )`
this satisfies the law of exponent, in which a^m / a^n is equal to a^(m-n). Therefore, we can write the equation as x^(3/5 - 1/4). Simplifying further, we will have
`x^{ (7)/(20) }`