If a fraction is in a bracket and is raised by the power of another fraction how would you evaluate it?
e.g (15/18)2/3 the 2/3 obviously raised as a power
Just looking for the rule as I can't find it!!!
$\displaystyle
(7/3)^{2/3} = (\sqrt[3]{7})^2/(\sqrt[3]{3})^2
$
note: the denominator in the origional exponent becomes the index in both numerator and denominator, and the numerator becomes the power to which result is raised in both numerator and denominator of the simplified expression.
$\displaystyle
(7/3)^{2/3} = (\sqrt[3]{7})^2/(\sqrt[3]{3})^2
$
$\displaystyle
= (1.91)^2/(1.44)^2
$
$\displaystyle
= 3.648/2.074
$
$\displaystyle
= 1.759 approx.
$