Prove that : (i)(√3×5−3÷3√3−1√5)×6√3×56=35(ii)932−3�

1.	Prove that : (i)(√3×5−3÷3√3−1√5)×6√3×56=35(ii)932−3×50−(181)−12=15(iii)(14)−2−3×823×40+(916)−12=163(iv)212×313×41410−15×535÷343×5−754−35×6=10(v)√14+(0.01)−12−(27)23=32(vi)2n+2n−12n+1−2n=32(vii)(64125)−23+1(256625)14+(√253√64)0=6116(viii)3−3×62×√9852×3√125×(15)−43×313=28√2(ix)(0.6)0−(0.1)−1(38)−1(32)3+(13)−1=−32
Answer» Prove that : $(i) (\sqrt{3 \times 5^{- 3}} \div \sqrt[3]{3^{- 1}} \sqrt{5}) \times \sqrt[6]{3 \times 5^{6}} = \frac{3}{5} (i i) 9^{\frac{3}{2}} - 3 \times 5^{0} - {(\frac{1}{81})}^{\frac{- 1}{2}} = 15 (i i i) {(\frac{1}{4})}^{- 2} - 3 \times 8^{\frac{2}{3}} \times 4^{0} + {(\frac{9}{16})}^{\frac{- 1}{2}} = \frac{16}{3} (i v) \frac{2^{\frac{1}{2}} \times 3^{\frac{1}{3}} \times 4^{\frac{1}{4}}}{10^{\frac{- 1}{5}} \times 5^{\frac{3}{5}}} \div \frac{3^{\frac{4}{3}} \times 5^{\frac{- 7}{5}}}{4^{\frac{- 3}{5}} \times 6} = 10 (v) \sqrt{\frac{1}{4}} + (0.01)^{\frac{- 1}{2}} - (27)^{\frac{2}{3}} = \frac{3}{2} (v i) \frac{2^{n} + 2^{n - 1}}{2^{n + 1} - 2^{n}} = \frac{3}{2} (v i i) {(\frac{64}{125})}^{\frac{- 2}{3}} + \frac{1}{{(\frac{256}{625})}^{\frac{1}{4}}} + {(\frac{\sqrt{25}}{\sqrt[3]{64}})}^{0} = \frac{61}{16} (v i i i) \frac{3^{- 3} \times 6^{2} \times \sqrt{98}}{5^{2} \times \sqrt[3]{\frac{1}{25}} \times (15)^{\frac{- 4}{3}} \times 3^{\frac{1}{3}}} = 28 \sqrt{2} (i x) \frac{(0.6)^{0} - (0.1)^{- 1}}{{(\frac{3}{8})}^{- 1} {(\frac{3}{2})}^{3} + {(\frac{1}{3})}^{- 1}} = - \frac{3}{2}$

Prove that : (i)(√3×5−3÷3√3−1√5)×6√3×56=35(ii)932−3×50−(181)−12=15(iii)(14)−2−3×823×40+(916)−12=163(iv)212×313×41410−15×535÷343×5−754−35×6=10(v)√14+(0.01)−12−(27)23=32(vi)2n+2n−12n+1−2n=32(vii)(64125)−23+1(256625)14+(√253√64)0=6116(viii)3−3×62×√9852×3√125×(15)−43×313=28√2(ix)(0.6)0−(0.1)−1(38)−1(32)3+(13)−1=−32

Answer»

Prove that :

$(i) (\sqrt{3 \times 5^{- 3}} \div \sqrt[3]{3^{- 1}} \sqrt{5}) \times \sqrt[6]{3 \times 5^{6}} = \frac{3}{5} (i i) 9^{\frac{3}{2}} - 3 \times 5^{0} - {(\frac{1}{81})}^{\frac{- 1}{2}} = 15 (i i i) {(\frac{1}{4})}^{- 2} - 3 \times 8^{\frac{2}{3}} \times 4^{0} + {(\frac{9}{16})}^{\frac{- 1}{2}} = \frac{16}{3} (i v) \frac{2^{\frac{1}{2}} \times 3^{\frac{1}{3}} \times 4^{\frac{1}{4}}}{10^{\frac{- 1}{5}} \times 5^{\frac{3}{5}}} \div \frac{3^{\frac{4}{3}} \times 5^{\frac{- 7}{5}}}{4^{\frac{- 3}{5}} \times 6} = 10 (v) \sqrt{\frac{1}{4}} + (0.01)^{\frac{- 1}{2}} - (27)^{\frac{2}{3}} = \frac{3}{2} (v i) \frac{2^{n} + 2^{n - 1}}{2^{n + 1} - 2^{n}} = \frac{3}{2} (v i i) {(\frac{64}{125})}^{\frac{- 2}{3}} + \frac{1}{{(\frac{256}{625})}^{\frac{1}{4}}} + {(\frac{\sqrt{25}}{\sqrt[3]{64}})}^{0} = \frac{61}{16} (v i i i) \frac{3^{- 3} \times 6^{2} \times \sqrt{98}}{5^{2} \times \sqrt[3]{\frac{1}{25}} \times (15)^{\frac{- 4}{3}} \times 3^{\frac{1}{3}}} = 28 \sqrt{2} (i x) \frac{(0.6)^{0} - (0.1)^{- 1}}{{(\frac{3}{8})}^{- 1} {(\frac{3}{2})}^{3} + {(\frac{1}{3})}^{- 1}} = - \frac{3}{2}$

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