Question

Which of the following is the simplified form of ^7 radical x • ^7 radical x • ^7 radical x

Answer 1

Answer: Option 1.

Explanation:

We need to remember that:

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

Then, having the expression:

`\sqrt[7]{x}*\sqrt[7]{x} *\sqrt[7]{x}`

We can rewrite it in this form:

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

According to the Product of powers property:

`(a^m)(a^n)=a^((m+n))`

Then, the simplied form of the given expression, is:

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

Answer 2

For this case we must find an expression equivalent to:

`\sqrt [7] {x} * \sqrt [7] {x} * \sqrt [7] {x}`

By definition of properties of powers and roots we have:

`\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}`

So, rewriting the given expression we have:

`x ^ {\frac {1} {7}} * x ^ {\frac {1} {7}} * x ^ {\frac {1} {7}} =`

To multiply powers of the same base we put the same base and add the exponents:

`x ^ {\frac {1} {7} + \frac {1} {7} + \frac {1} {7}} =\\x ^ {\frac {3} {7}}`

Answer:

Option 1