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

The correct answer is a

Answer 2

Answer:

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

Step-by-step explanation:

We want to simplify

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

Recall that,

$a^m\times a^n=a^{m+n}$

So weneed to write one base and add the exponents,

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

We collect LCM in the exponent to get,

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

We simplify to obtain,

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

The correct answer is A.