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 ?

Answer 1

x
`(3)/(7)`

Explanation:

Answer 2

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

Explanation:

I'd assume your question is to simplify the expression
`\sqrt[7]{x}*\sqrt[7]{x}*\sqrt[7]{x}`

There are 2 rules of exponents we are going to use to simplify this expression:

1. 
   `\sqrt[n]{a} = a^{(1)/(n)}`, and
2. 
   `a^(m)*a^(n)=a^(m+n)`

Using RULE 1, we can write the radicals [expression with roots] into exponential form [with a fractional exponent] like this:

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

Now, the bases are same,
`x`, and we have 3 powers. Using RULE 2, we can add the powers like this:

`x^{(1)/(7)+(1)/(7)+(1)/(7)}\\=x^{(3)/(7)}`

This is the simplified form.