Simplify the following:
(8116)−34\Big(\dfrac{81}{16}\Big)^{-\dfrac{3}{4}}(1681)−43
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Given,
⇒(8116)−34=(1681)34=(2434)34=24×3434×34=2333=827.\Rightarrow \Big(\dfrac{81}{16}\Big)^{-\dfrac{3}{4}} = \Big(\dfrac{16}{81}\Big)^{\dfrac{3}{4}} \\[1em] = \Big(\dfrac{2^4}{3^4}\Big)^{\dfrac{3}{4}} = \dfrac{2^{4 \times \dfrac{3}{4}}}{3^{4 \times \dfrac{3}{4}}} \\[1em] = \dfrac{2^3}{3^3} = \dfrac{8}{27}.⇒(1681)−43=(8116)43=(3424)43=34×4324×43=3323=278.
Hence, (8116)−34=827.\Big(\dfrac{81}{16}\Big)^{-\dfrac{3}{4}} = \dfrac{8}{27}.(1681)−43=278.
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Solve the following equation :
3x + 1 = 27.34
42x=(163)−6y=(8)24^{2x} = (\sqrt[3]{16})^{-\frac{6}{y}} = (\sqrt{8})^242x=(316)−y6=(8)2
3x - 1 × 52y - 3 = 225
8x + 1 = 16y + 2, (12)3+x=(14)3y\Big(\dfrac{1}{2}\Big)^{3 + x} = \Big(\dfrac{1}{4}\Big)^{3y}(21)3+x=(41)3y
