Question

Which expression is equivalent to 6^-3?
6^3
3^6
3sqrt6
(1/6)^3

Answer 1

The correct answer option is D. ( 1 / 6 ) ^ 3.

Explanation:

We are given the following expression and we are to determine whether which of the given answer options is equivalent to this:

`6 ^ { - 3 }`

Rewriting this as a fraction to get:

`\frac { 1 } { 6 ^ 3 }`

Therefore, the correct answer option is D. ( 1 / 6 ) ^ 3.

Answer 2

For this case we must find an expression equivalent to
`6 ^ {- 3}`

By definition of power properties we have to:

`a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}`

So, we can rewrite the given expression as:

`6 ^ {3} = \frac {1} {6 ^ 3}`

This is equivalent to:

`(\frac {1} {6}) ^ 3`

Answer:

Option D