(i) (3^1/2+1/6.5^{-3/2 +1}) / (3^-1/3.5^1/2)

₌₍₃^2/3.5^-1/2) / (3^-1/3.5^1/2)

₌₍₃^{2/3 + 1/3}) / (5^{1/2 +1/2})

_=3/5

_{(ii) (3}² )^3/2 -3.1 – (1/9²)^-1/2

_{= 3}³ -3 -9

_{=27 -3 -9}

_=27-12

₌₁₅

_{(iii) 2}^(-2)(-2) -3.8^2/3 +(3/4)^-1

₌₂⁴ -3.2² + 4/3

_{=16 -12 + 4/3}

_=16/3

_{(iv) [(2.3}^1/3)/(2^-1/5 5^2/5)] × (2^-1/5.3)/ (3^4/3.5^7/5)

_{= 2.3}^{1/3 +1 -4/3} / 5^2/5-7/5

_{= 2.5}

₌₁₀

_{(v) 1/2 + 1/(0.01)}^1/2 -3²

_{=1/2 + 10 – 9}

_{=1/2 + 1}

_=3/2

_{(vi) (2}ⁿ + 2^n-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)/ (5^4/3.(15)^-4/3‑.3^1/3) =28(2)^1/2

₍₃^-3.36.7(2)^1/2)/ (5^4/3-4/3.(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}