Question

What is the value of (2/3)^-4 A. -81/16 B. -16/81 C. 16/81 D. 81/16

Answer 1

For this case, we must find the value of the following expression:

$(\frac {2} {3}) ^ {- 4}$

By properties of powers we have that:

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

Thus, we can rewrite the expression as:

$\frac {1} {(\frac {2} {3}) ^ 4} =\\\frac {3 ^ 4} {2 ^ 4} =\\\frac {81} {16}$

So, we have to:

$(\frac {2} {3}) ^ {- 4} = \frac {81} {16}$

Answer:

$\frac {81} {16}$

Option D