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Show that:(i) ∛(729)/ ∛ (1000) = ∛(729/1000)(ii) ∛(-512)/ ∛ (343) = ∛(-512/343) |
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Answer» (i) ∛(729)/ ∛(1000) = ∛(729/1000) L.H.S= ∛(729)/ ∛(1000) ∛(729)/ ∛(1000) = ∛(9×9×9)/ ∛(10×10×10) = ∛(93/103) = 9/10 R.H.S = ∛(729/1000) ∛(729/1000) = ∛(9×9×9/10×10×10) = ∛ (93/103) = 9/10 L.H.S = R.H.S (ii) ∛(-512)/ ∛(343) = ∛(-512/343) L.H.S = ∛(-512)/ ∛ (343) ∛(-512)/ ∛(343) = ∛-(8×8×8)/ ∛(7×7×7) = ∛-(83/73) = -8/7 R.H.S = ∛(-512/343) ∛(-512/343) =∛-(8×8×8/7×7×7) = ∛-(83/73) = -8/7 L.H.S = R.H.S |
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