Question

$\frac{\sqrt{x^3}\times \sqrt[3]{3x^5}}{\sqrt[5]{5x^3}}\times \sqrt[30]{30x^{77}}=$

• A. $x^{76/15}$
• B. $x^{78/15}$
• C. $x^{79/15}$
• D. $x^{77/15}$

Answer 1

Answer: (D)

$x^{77/15}$

We have, $\frac{\sqrt{x^3}\times \sqrt[3]{3x^5}}{\sqrt[5]{5x^3}}\times \sqrt[30]{30x^{77}}$

$\Rightarrow$ $\sqrt{x^3}\times \sqrt[3]{3x^5}\times \frac{\sqrt[30]{30x^{77}}}{\sqrt[5]{5x^3}}$

$=x^{\frac{3}{2}}\times x^{\frac{5}{3}}\times \frac{x^{\frac{77}{30}}}{x^{\frac{3}{5}}}$

$=x^{\frac{3}{2}+\frac{5}{3}}\times x^{\frac{77}{30}-\frac{3}{5}}$ ...$[\because x^m\times x^n=x^{m+n};\frac{x^m}{x^n}=x^{m-n}]$

$=x^{\frac{19}{6}}\times x^{\frac{59}{30}}$

$=x^{\frac{19}{6}+\frac{59}{30}}$

$=x^{\frac{77}{15}}$

$\therefore$ $\frac{\sqrt{x^3}\times \sqrt[3]{3x^5}}{\sqrt[5]{5x^3}}\times \sqrt[30]{30x^{77}}=x^{77/15}$