Prove that:
(i)
(ii) 93/2 -3× 50 - = 15
(iii) -3×82/3 ×40+
(iv) = 10
(v) + (0.01)-1/2 – (27)2/3 =
(vi)
(vii)
(viii) = 28
(ix)
(i) (31/2+1/6.5-3/2 +1) / (3-1/3.51/2)
=(32/3.5-1/2) / (3-1/3.51/2)
=(32/3 + 1/3) / (51/2 +1/2)
=3/5
(ii) (32 )3/2 -3.1 – (1/92)-1/2
= 33 -3 -9
=27 -3 -9
=27-12
=15
(iii) 2(-2)(-2) -3.82/3 +(3/4)-1
=24 -3.22 + 4/3
=16 -12 + 4/3
=16/3
(iv) [(2.31/3)/(2-1/5 52/5)] × (2-1/5.3)/ (34/3.57/5)
= 2.31/3 +1 -4/3 / 52/5-7/5
= 2.5
=10
(v) 1/2 + 1/(0.01)1/2 -32
=1/2 + 10 – 9
=1/2 + 1
=3/2
(vi) (2n + 2n-1)/ ) (2n+1 - 2n)
=2n(1 + 2-1 ) / 2n (2-1)
= [1 + (1/2)]/1
=1 + 1/2
=3/2
(vii) (125/64)2/3 + (625/256)1/4 + ( 5/4)
=(5/4)2 + 5/4 + 5/4
=25/16 + 5/4 + 5/4
=65/16
(viii) (3-3.62.7(2)1/2)/ (54/3.(15)-4/3‑.31/3) =28(2)1/2
(3-3.36.7(2)1/2)/ (54/3-4/3.(3)-1)
(3-2.36.7(2)1/2)/ (50)
1/9.36.7(2)1/2
28
(ix) {1- 1/0.1}/ { (3/8)-1(3/2)3 + (-1/3)-1
=1-10/{ (8/3)(3/2)3 + (-3)
=-9/(32-3)
= -3/2