Simplify the following:
72n+3−(49)n+2((343)n+1)23\dfrac{7^{2n + 3} - (49)^{n + 2}}{((343)^{n + 1})^{\dfrac{2}{3}}}((343)n+1)3272n+3−(49)n+2
83 Likes
Given,
⇒72n+3−(49)n+2((343)n+1)23⇒72n+3−(72)n+2((73)n+1)23⇒72n+3−72n+473×(n+1)×23⇒72n.73−72n.7472(n+1)⇒343.72n−2401.72n72n+2⇒72n(343−2401)72n.72⇒−205849=−42.\Rightarrow \dfrac{7^{2n + 3} - (49)^{n + 2}}{((343)^{n + 1})^{\dfrac{2}{3}}} \\[1em] \Rightarrow \dfrac{7^{2n + 3} - (7^2)^{n + 2}}{((7^3)^{n + 1})^{\dfrac{2}{3}}} \\[1em] \Rightarrow \dfrac{7^{2n + 3} - 7^{2n + 4}}{7^{3 \times (n + 1) \times \dfrac{2}{3}}} \\[1em] \Rightarrow \dfrac{7^{2n}.7^3 - 7^{2n}.7^{4}}{7^{2(n + 1)}} \\[1em] \Rightarrow \dfrac{343.7^{2n} - 2401.7^{2n}}{7^{2n + 2}} \\[1em] \Rightarrow \dfrac{7^{2n}(343 - 2401)}{7^{2n}.7^2} \\[1em] \Rightarrow \dfrac{-2058}{49} = -42.⇒((343)n+1)3272n+3−(49)n+2⇒((73)n+1)3272n+3−(72)n+2⇒73×(n+1)×3272n+3−72n+4⇒72(n+1)72n.73−72n.74⇒72n+2343.72n−2401.72n⇒72n.7272n(343−2401)⇒49−2058=−42.
Hence, 72n+3−(49)n+2((343)n+1)23\dfrac{7^{2n + 3} - (49)^{n + 2}}{((343)^{n + 1})^{\dfrac{2}{3}}}((343)n+1)3272n+3−(49)n+2 = -42.
Answered By
45 Likes
(32)25×(4)−12×(8)132−2÷(64)−13\dfrac{(32)^{\dfrac{2}{5}} \times (4)^{-\dfrac{1}{2}} \times (8)^{\dfrac{1}{3}}}{2^{-2} ÷ (64)^{-\dfrac{1}{3}}}2−2÷(64)−31(32)52×(4)−21×(8)31
52(x+6)×(25)−7+2x(125)2x\dfrac{5^{2(x + 6)} \times (25)^{-7 + 2x}}{(125)^{2x}}(125)2x52(x+6)×(25)−7+2x
(27)43+(32)0.8+(0.8)−1(27)^{\dfrac{4}{3}} + (32)^{0.8} + (0.8)^{-1}(27)34+(32)0.8+(0.8)−1
(32−5)13(32+5)13(\sqrt{32} - \sqrt{5})^{\dfrac{1}{3}}(\sqrt{32} + \sqrt{5})^{\dfrac{1}{3}}(32−5)31(32+5)31
