5×3−3×5×36656×3\dfrac{\sqrt{5 \times 3^{-3}} \times \sqrt[6]{5 \times 3^6}}{\sqrt[6]{5} \times \sqrt{3}}65×35×3−3×65×36 =
35\sqrt{\dfrac{3}{5}}53
53\sqrt{\dfrac{5}{3}}35
35\dfrac{3}{5}53
53\dfrac{\sqrt{5}}{3}35
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Given,
5×3−3×5×36656×3\dfrac{\sqrt{5 \times 3^{-3}} \times \sqrt[6]{5 \times 3^6}}{\sqrt[6]{5} \times \sqrt{3}}65×35×3−3×65×36
Simplifying the expression:
⇒5×3−3×56×36656×3⇒5×(3−3)12×36×163⇒5×3−32×31312⇒5×3−32+1−12⇒5×3−3+2−12⇒5×3−22⇒5×3−1⇒53.\Rightarrow \dfrac{\sqrt{5} \times \sqrt{3^{-3}} \times \sqrt[6]{5} \times \sqrt[6]{3^6}}{\sqrt[6]{5} \times \sqrt{3}} \\[1em] \Rightarrow \dfrac{\sqrt{5} \times {(3^{-3})}^{\dfrac{1}{2}} \times {3}^{6 \times \dfrac{1}{6}}}{\sqrt{3}} \\[1em] \Rightarrow \dfrac{\sqrt{5} \times {3}^{\dfrac{-3}{2}} \times {3^1}}{{3}^{\dfrac{1}{2}}} \\[1em] \Rightarrow \sqrt{5} \times {3}^{\dfrac{-3}{2} + 1 - \dfrac{1}{2}} \\[1em] \Rightarrow \sqrt{5} \times {3}^{\dfrac{-3 + 2 - 1}{2}} \\[1em] \Rightarrow \sqrt{5} \times {3}^{\dfrac{-2}{2}} \\[1em] \Rightarrow \sqrt{5} \times {3}^{-1} \\[1em] \Rightarrow \dfrac {\sqrt{5}}{3}.⇒65×35×3−3×65×636⇒35×(3−3)21×36×61⇒3215×32−3×31⇒5×32−3+1−21⇒5×32−3+2−1⇒5×32−2⇒5×3−1⇒35.
Hence, option 4 is the correct option.
Answered By
128×32(−43)128 \times 32^{\Big(-\dfrac{4}{3}\Big)}128×32(−34) =
43\sqrt[3]{4}34
23\sqrt[3]{2}32
8
2
[(a43)−32]−12\Big[\Big(\sqrt[3]{a^4}\Big)^{\dfrac{-3}{2}}\Big]^{\dfrac{-1}{2}}[(3a4)2−3]2−1 =
a
a2
1a\dfrac{1}{a}a1
1a2\dfrac{1}{a^2}a21
(81)0.13 × (81)0.12 =
1
3
3\sqrt{3}3
13\dfrac{1}{\sqrt{3}}31
If 3x = 3-x, then (1.2)x =
0
1.2
1.44
