Question : The simplified value of the following is:
$\left (\frac{3}{15}a^{5}b^{6}c^{3}\times \frac{5}{9}ab^{5}c^{4} \right )\div \frac{10}{27}a^{2}bc^{3}$.
Option 1: $\frac{9a^{2}bc^{4}}{10}$
Option 2: $\frac{3ab^{4}c^{3}}{10}$
Option 3: $\frac{3a^{4}b^{10}c^{4}}{10}$
Option 4: $\frac{1a^{4}b^{4}c^{10}}{10}$
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Correct Answer: $\frac{3a^{4}b^{10}c^{4}}{10}$
Solution :
Given equation:
$( \frac{3}{15}a^{5}b^{6}c^{3}\times \frac{5}{9}ab^{5}c^{4})\div \frac{10}{27}a^{2}bc^{3}$
= $( \frac{a^6b^{11}c^7}{9}) \div ( \frac{10}{27}a^2bc^3)$
= $\frac{27a^6b^{11}c^7}{9\times10 a^2bc^3}$
= $\frac{27a^6b^{11}c^7}{90a^2bc^3}$
= $\frac{3a^4b^{10}c^4}{10}$
Hence, the correct answer is $\frac{3a^4b^{10}c^4}{10}$.
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