Question

Simplify: $\sqrt{\frac{81a^4}{49b^8}}\times \frac{3b}{5ac}\times \sqrt[3]{3\frac{125c^6}{64b^9}}$

• A. $\frac{27a{c}^2}{14b^4}$
• B. $\frac{27ac}{28b^6}$
• C. $\frac{45a^{2}c}{56b^4}$
• D. $\frac{45ac}{56b^6}$

Answer 1

The correct option is B $\frac{27ac}{28b^6}$

$\sqrt{\frac{81a^4}{49b^8}}\times \frac{3b}{5ac}\times \sqrt[3]{3\frac{125c^6}{64b^9}}$

$=\frac{9a^2}{7b^4}\times \frac{3b}{5ac}\times \frac{5c^2}{4b^3}$

$=\frac{9a^2\times 3b\times 5c^2}{7b^4\times 5ac\times 4b^3}$

$=\frac{27a^{2}b{c}^2}{28a{b}^{7}c}$

$=\frac{27ac}{28b^6}$