Question

Simplify the following if possible. Write your answer with only positive exponents. (−64)−2/3

Answer 1

For this case we have that by definition of power properties

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

So:

`(-64) ^ {- \frac {2} {3}}`

It can be written as:

`- \frac {1} {64 ^ {\frac {2} {3}}}`

If we decompose 64 we have:

`64 = 2 * 2 * 2 * 2 * 2 * 2 = 2 ^ 6`

So:

`- \frac {1} {(2 ^ 6) ^ {\frac {2} {3}}}`

Multiplying powers:

`- \frac {1} {(2 ^ 6) ^ {\frac {2} {3}}} = - \frac {1} {2 ^ 4} = - \frac {1} {16}`

Answer:

`- \frac {1} {16}`