Question

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

Answer 1

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

Answer 2

Answer: Option 1.

Step-by-step explanation:

We need to remember that:

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

Then, having the expression:

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

We can rewrite it in this form:

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

According to the Product of powers property:

$(a^m)(a^n)=a^{(m+n)}$

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

$=x^{(\frac{1}{7}+\frac{1}{7}+\frac{1}{7})}=x^\frac{3}{7}$