Simplify :
(27)2n3×(8)−n6(18)−n2\dfrac{(27)^{\dfrac{2n}{3}} \times (8)^{-\dfrac{n}{6}}}{(18)^{-\dfrac{n}{2}}}(18)−2n(27)32n×(8)−6n
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Given,
Simplifying the expression :
⇒[(3)3]2n3×[(2)3]−n6[(3)2×2]−n2⇒[(3)2n]×(2)−n2[(3)2]−n2×(2)−n2⇒(3)2n3−n⇒(3)2n−(−n)⇒(3)2n+n⇒33n.\Rightarrow \dfrac{[(3)^3]^{\dfrac{2n}{3}} \times [(2)^3]^{-\dfrac{n}{6}}}{[(3)^2 \times 2]^{-\dfrac{n}{2}}} \\[1em] \Rightarrow \dfrac{[(3)^{2n}] \times (2)^{-\dfrac{n}{2}}}{[(3)^2]^{-\dfrac{n}{2}} \times (2)^{-\dfrac{n}{2}}} \\[1em] \Rightarrow \dfrac{(3)^{2n}}{3^{-n}} \\[1em] \Rightarrow (3)^{2n - (-n)} \\[1em] \Rightarrow (3)^{2n + n} \\[1em] \Rightarrow 3^{3n}.⇒[(3)2×2]−2n[(3)3]32n×[(2)3]−6n⇒[(3)2]−2n×(2)−2n[(3)2n]×(2)−2n⇒3−n(3)2n⇒(3)2n−(−n)⇒(3)2n+n⇒33n.
Hence, (27)2n3×(8)−n6(18)−n2=33n\dfrac{(27)^{\dfrac{2n}{3}} \times (8)^{-\dfrac{n}{6}}}{(18)^{-\dfrac{n}{2}}} = 3^{3n}(18)−2n(27)32n×(8)−6n=33n.
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