Question

What is the multiplicative inverse of (2/3)raised to power -3

Answer 1

the multiplicative inverse is 3/2 raised to power 3

Answer 2

Multiplicative inverse is also known as RECIPROCAL.

${ (\frac{2}{3}) }^{ - 3} \times x = 1$
This is the basic/common/ the only equation which a number and it's reciprocal satisfy.

$x = { (\frac{3}{2}) }^{ - 3}$
If we don't want the negative exponent, we can say that,

${ (\frac{2}{3}) }^{3} \: is \: the \: reciprocl \: of \: { (\frac{3}{2}) }^{3}$
I.e.,
$\frac{8}{27} \: is \: the \: reciprocal \: of \: \frac{27}{8}$