Question

Which of the following represents sixth root of x to the fifth power in exponential form?

5x6
6x5
x to the 5 sixths power
x to the 6 fifths power

Answer 1

x to the 5 sixth power

Answer 2

`\sqrt[6]{x}=x^{(5)/(6)`

Option 3 is correct.

Explanation:

`\text{Given the expression in words which represents sixth root of x to the fifth power }`

we have to write in exponential form.

Step 1: sixth root of x can be written as

`\sqrt[6]{x}=x^{(1)/(6)`

Step 2: Fifth power of sixth root of x

`(x^{(1)/(6))^5`

`\text{As, }(x^m)^n=x^(mn)`

`(x^{(1)/(6)})^5=x^{{5* (1)/(6)}}=x^{(5)/(6)}`

which implies x to the 5 sixths power.

Option 3 is correct.