Simplify the following:
(3x2)−3×(x9)23(3x^2)^{-3} \times (x^9)^{\dfrac{2}{3}}(3x2)−3×(x9)32
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Given,
⇒(3x2)−3×(x9)23=(13x2)3×[(x3)3]23=127x6×(x3)3×23=127x6×x6=127.\Rightarrow (3x^2)^{-3} \times (x^9)^{\dfrac{2}{3}} = \Big(\dfrac{1}{3x^2}\Big)^3 \times [(x^3)^3]^{\dfrac{2}{3}} \\[1em] = \dfrac{1}{27x^6} \times (x^3)^{3 \times \dfrac{2}{3}} \\[1em] = \dfrac{1}{27x^6} \times x^6 = \dfrac{1}{27}.\\[1em]⇒(3x2)−3×(x9)32=(3x21)3×[(x3)3]32=27x61×(x3)3×32=27x61×x6=271.
Hence, (3x2)−3×(x9)23=127.(3x^2)^{-3} \times (x^9)^{\dfrac{2}{3}}= \dfrac{1}{27}.(3x2)−3×(x9)32=271.
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