Question

Which of the following is the simplified form ofthe seventh root of x times the seventh root of x times the seventh root of x? a. x3/7 b. x1/7 c. x3/21 d. 21 root of x

Answer 1

`x^{(3)/(7)}`

Explanation:

Given : seventh root of x times the seventh root of x times the seventh root of x

To Find :Which of the following is the simplified form

Solution:

Seventh root of x=
`\sqrt[7]{x} =x^{(1)/(7)}`

Now we are given that seventh root of x times the seventh root of x times the seventh root of x

`\Rightarrow x^{(1)/(7)} * x^{(1)/(7)} * x^{(1)/(7)}`

Property :
`a^x * a^y =a^(x+y)`

So,
`\Rightarrow x^{(1)/(7)+(1)/(7) + (1)/(7)}`

`\Rightarrow x^{(3)/(7)}`

So, the simplified form of the seventh root of x times the seventh root of x times the seventh root of x is
`x^{(3)/(7)}`

So, Option A is true.