Question

MEDAL::What is the simplified form of the seventh root of x to the fifth power times the seventh root of x to the fifth power? how do i solve this???

Answer 1

remember
(x^m)(x^n)=x^(m+n)

and

`\sqrt[n]{x^m} =x^{ (m)/(n) }` so



`(\sqrt[7]{x^5})(\sqrt[7]{x^5})` =

`(x^{ (5)/(7))(x^{ (5)/(7)) }` =

`x^((5)/(7)+(5)/(7))` =

`x^((10)/(7))`=

`(x^ (7)/(7) )(x^ (3)/(7))`=
(x)(
`x^ (3)/(7)`=

`x \sqrt[7]{x^3}`

Answer 2

The mathematical expression of the given above is,
(x^1/7)^5 x (x^17)^5
Take note that for (x^n)^m, the answer is x^nm. For our expression above,
(x^5/7) x (x^5/7)
Another rule for exponent is that for (x^n) x (x^m) the answer would be x^(n + m). For the expression,
x^10/7