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:

$- \frac {1} {16}$