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1a]
V27
= V(9 × 3)
= V9V3
= 3V3
b]
V44
= V(4 × 11)
= V4V11
= 2V11
c]
V50
= V(25 × 2)
= V25V2
= 5V2
d]
V96
= V(16 × 6)
= V16V6
= 4V6
e]
4V99
= 4V(9 × 11)
= 4V9V11
= 4(3)V11
= 12V11
f]
2V500
= 2V(100 × 5)
= 2V100V5
= 2(10)V5
= 20V5
2a]
V75 – V48
= V(25 × 3) – V(16 × 3)
= V25V3 – V16V3
= 5V3 – 4V3
= V3
b]
V125 – 2V5
= V(25 × 5) – 2V5
= V25V5 – 2V5
= 5V5 – 2V5
= 3V5
c]
V5 – 3V5 + 6V5
= 4V5
d]
V2 + V8 + V32
= V2 + V(4 × 2) + V(16 × 2)
= V2 + V4V2 + V16V2
= V2 + 2V2 + 4V2
= 7V2
e]
2V3 – V27 + V48
= 2V3 – V(9 × 3) + V(16 × 3)
= 2V3 – V9V3 + V16V3
= 2V3 – 3V3 + 4V3
= 3V3
3a]
8/V2
= (8/V2) × (V2/V2)
= (8V2)/2
= 4V2
b]
5/V3
= (5/V3) × (V3/V3)
= (5V3)/3
= 5/3 V3
c]
3/V12
= 3/[V(4 × 3)]
= 3/(V4V3)
= 3/(2V3)
= [3/(2V3)] × (V3/V3)
= (3V3)/6
= 1/2 V3
d]
6/V27
= 6/[V(9 × 3)]
= 6/(V9V3)
= 6/(3V3)
= [6/(3V3)] × (V3/V3)
= (6V3)/9
= 2/3 V3
e]
2/(1 – V2)
= [2/(1 – V2)] × [(1 + V2)/(1 + V2)]
= (2 + 2V2)/(1 – 2)
= (2 + 2V2)/(-1)
= -2 – 2V2
f]
V5/(V2 – 3)
= [V5/(V2 – 3)] × [(V2 + 3)/(V2 + 3)]
= (V10 + 3V5)/(2 – 9)
= (V10 + 3V5)/(-7)
= -1/7 (V10 + 3V5)
g]
(3 – V2)/(3 + V2)
= [(3 – V2)/(3 + V2)] × [(3 – V2)/(3 – V2)]
= (9 – 6V2 + 2)/(9 – 2)
= (11 – 6V2)/7
= 1/7 (11 – 6V2)
h]
(4 + V3)/(4 – V3)
= [(4 + V3)/(4 – V3)] × [(4 + V3)/(4 + V3)]
= (16 + 8V3 + 3)/(16 – 3)
= (19 + 8V3)/13
= 1/13 (19 + 8V3)
4a]
2^(2/3)
= 3^V(2^2)
= 3^V4
b]
4^(2/7)
= 7^V(4^2)
= 7^V16
c]
6^3/2
= V(6^3)
= V216