Evaluate :
(278)23−(14)−2+50\Big(\dfrac{27}{8}\Big)^{\dfrac{2}{3}} - \Big(\dfrac{1}{4}\Big)^{-2} + 5^0(827)32−(41)−2+50
33 Likes
Simplifying the expression :
⇒(278)23−(14)−2+50=[(32)3]23−(122)−2+50=(32)3×23−(22)2+1=(32)2−24+1=94−16+1=9−64+44=−514.\Rightarrow \Big(\dfrac{27}{8}\Big)^{\dfrac{2}{3}} - \Big(\dfrac{1}{4}\Big)^{-2} + 5^0 = \Big[\Big(\dfrac{3}{2}\Big)^3\Big]^{\dfrac{2}{3}} - \Big(\dfrac{1}{2^2}\Big)^{-2} + 5^0\\[1em] = \Big(\dfrac{3}{2}\Big)^{3 \times \dfrac{2}{3}} - (2^2)^2 + 1 \\[1em] = \Big(\dfrac{3}{2}\Big)^2 - 2^4 + 1 \\[1em] = \dfrac{9}{4} - 16 + 1 \\[1em] = \dfrac{9 - 64 + 4}{4} \\[1em] = -\dfrac{51}{4}.⇒(827)32−(41)−2+50=[(23)3]32−(221)−2+50=(23)3×32−(22)2+1=(23)2−24+1=49−16+1=49−64+4=−451.
Hence, (278)23−(14)−2+50=−514\Big(\dfrac{27}{8}\Big)^{\dfrac{2}{3}} - \Big(\dfrac{1}{4}\Big)^{-2} + 5^0 = -\dfrac{51}{4}(827)32−(41)−2+50=−451.
Answered By
17 Likes
Simplify :
(3x2)−3×(x9)23(3x^2)^{-3} \times (x^9)^{\dfrac{2}{3}}(3x2)−3×(x9)32
14+(0.01)−12−(27)23\sqrt{\dfrac{1}{4}} + (0.01)^{-\dfrac{1}{2}} - (27)^{\dfrac{2}{3}}41+(0.01)−21−(27)32
Simplify the following and express with positive index :
(3−42−8)14\Big(\dfrac{3^{-4}}{2^{-8}}\Big)^{\dfrac{1}{4}}(2−83−4)41
(27−39−3)15\Big(\dfrac{27^{-3}}{9^{-3}}\Big)^{\dfrac{1}{5}}(9−327−3)51
