S i m p l i f y 256 x 16 81 y 4 - 1 / 4

Dear Student,

Answer (i):

Simplifying:

=256 x1681 y4-14=44 x1634 y4-14                     as 256=44 and 81=34=44×-14 x16×-1434×-14 y4×-14        as xab=xa×b=4-1 x-43-1 y-1=3y4x4                                    as x-1=1x


Answer (ii):

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, AOC=2ABC=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,  OAC=OCA=x

As the sum of interior angles of triangle is 180, thus in AOC
OAC+OCA+AOC=180or, x+x+100=180or, 2x=80or, x=40


Answer (iii):

Let's say;

S=0.1233333....or, 10S=1.233333....         Mutlyiplying both the sides by 10or, 10S-S=1.23333.....-0.123333....or, 9S=1.110000....or, 9S=1.11or, S=1.119or, S=111900

Hope this information will clear your doubts about the topic.

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Regards

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