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

Answer:

$x^{\frac{3}{7}}$

Step-by-step 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. $\sqrt[n]{a} = a^{\frac{1}{n}}$, 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:

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

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

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

This is the simplified form.

Answer 2

Answer:

x$\frac{3}{7}$

Step-by-step explanation: