Question

Which expression can be simplified as 1/n^18

A. (n^2)^9
B. (n^-9)^-2
C. (n^-6)^-3
D. (n^-3)^6

Answer 1

(n^-3)^6=n^-18=1/n^18

the answer is D

Answer 2

Option D is correct.

`(n^(-3))^(6)` can be simplified as 1/n^18

Explanation:

Using exponent rules:

`(a^n)^m = a^(nm)`

`(1)/(a^n) = a^(-n)`

Given the expression:

`(1)/(n^(18))`

Apply the exponent rules:

⇒
`n^(-18)`

A.

`(n^2)^9`

⇒
`n^(2 \cdot 9) = n^(18)`

B.

`(n^(-9))^(-2)`

⇒
`n^(-2 \cdot -9) = n^(18)`

C.

`(n^(-6))^(-3)`

⇒
`n^(-6 \cdot -3) = n^(18)`

D.

`(n^(-3))^(6)`

⇒
`n^(-3 \cdot 6) = n^(-18)`

Therefore,
`(n^(-3))^(6)` expression can be simplified as
`n^(-18)`