# $Simplify\phantom{\rule{0ex}{0ex}}{\left[\frac{256{x}^{16}}{81{y}^{4}}\right]}^{-1/4}$

Dear Student,

Simplifying:

The figure can we redrawn as:

In a circle, the angle at the centre of the circle is twice the angle subtended by the same arc on the circumference. This is called the Angle at the Centre theorem.

Hence, $\angle AOC=2\angle ABC=2×50=100$
Now, as $△AOC$ is an isosceles triangle as AO = OC which are the radius of the circle.
And in an isosceles triangle, angle opposite to equal sides are always equal,
Hence,  $\angle OAC=\angle OCA=x$

As the sum of interior angles of triangle is 180, thus in $△AOC$