| The value of \[{{(125)}^{\frac{4}{3}}}\div {{(5)}^{3}}\times {{\left( \frac{1}{8} \right)}^{\frac{4}{3}}}\times {{(\sqrt{3})}^{4}}\] |
A) (a)\[12\]
B) \[\frac{44}{39}\]
C) \[16\]
D) \[\frac{45}{8}\]
Correct Answer: D
Solution :
| \[{{(125)}^{4/3}}\div {{(5)}^{3}}\times {{\left( \frac{1}{8} \right)}^{4/3}}\times {{(\sqrt{3})}^{4}}\] |
| \[={{({{5}^{3}})}^{4/3}}\div {{(5)}^{3}}\times {{\left( \frac{1}{2} \right)}^{3\times \frac{4}{3}}}\times {{(\sqrt{3})}^{4}}\] |
| \[={{(5)}^{4}}\times \frac{1}{{{(5)}^{3}}}\times {{\left( \frac{1}{2} \right)}^{4}}\times {{(\sqrt{3})}^{4}}\] |
| \[=625\times \frac{1}{125}\times \frac{1}{8}\times 9=5\times \frac{1}{8}\times 9=\frac{45}{8}\] |
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