Question

Which of the following is equivalent to 36^(-1/2)?
A)-18
B)-6
C)1/18
D)1/6

Answer 1

Option D is correct.

`(1)/(6)` is equivalent to
`(36)^{(-1)/(2)}`

Explanation:

Given :
`(36)^{(-1)/(2)}`

Find the equivalent expression:

Using rule:

• 
  `(a^n)^m= a^(nm)`
• 
  `a^(-n) =(1)/(a^n)`

`(36)^{(-1)/(2)}`

⇒
`(6^2)^{(-1)/(2))`

⇒
`(6)^{2 * (-1)/(2)}`

⇒
`6^(-1)` =
`(1)/(6)`

therefore, the following equivalent to
`(36)^{(-1)/(2)}` is,
`(1)/(6)`

Answer 2

The correct option is D. The value of given expression is equivalent to
`(1)/(6)`.

Explanation:

The given expression is

`36^{-(1)/(2)}`

`36^{-(1)/(2)}=\frac{1}{36^{(1)/(2)}}`
`[\because a^(-x)=(1)/(a^x)]`

`36^{-(1)/(2)}=(1)/(√(36))`
`[\because a^{(1)/(2)}=√(a)]`

`36^{-(1)/(2)}=(1)/(6)`

Therefore correct option is D. The value of given expression is equivalent to
`(1)/(6)`.