Simplify the following:
(8x4)13÷x13(8x^4)^{\dfrac{1}{3}} ÷ x^{\dfrac{1}{3}}(8x4)31÷x31
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Given,
⇒(8x4)13÷x13=(8)13(x4)13×1(x)13=(23)13.(x)43.(x)−13=2.(x)43−13=2.(x)33=2x.\Rightarrow (8x^4)^{\dfrac{1}{3}} ÷ x^{\dfrac{1}{3}} = (8)^{\dfrac{1}{3}} (x^4)^{\dfrac{1}{3}} \times \dfrac{1}{(x)^{\dfrac{1}{3}}} \\[1em] = (2^3)^{\dfrac{1}{3}}.(x)^{\dfrac{4}{3}}.(x)^{-\dfrac{1}{3}} \\[1em] = 2.(x)^{\dfrac{4}{3} - \dfrac{1}{3}} = 2.(x)^{\dfrac{3}{3}} = 2x.⇒(8x4)31÷x31=(8)31(x4)31×(x)311=(23)31.(x)34.(x)−31=2.(x)34−31=2.(x)33=2x.
Hence, (8x4)13÷x13(8x^4)^{\dfrac{1}{3}} ÷ x^{\dfrac{1}{3}}(8x4)31÷x31 = 2x.
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