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 ?

a. x to the 3 over seventh power
b. x to the 1 over seventh power
c. x to the 3 over 21st power
d. the 21st root of x

Answer 1

The correct answer is a

Answer 2

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

Explanation:

We want to simplify

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

Recall that,

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

So weneed to write one base and add the exponents,

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

We collect LCM in the exponent to get,

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

We simplify to obtain,

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

The correct answer is A.