Question

Fill in the blanks
$\frac{\sqrt{x^3}\times \sqrt[3]{3x^5}}{\sqrt[5]{5x^3}}\times \sqrt[30]{30x^{77}}=$___.

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

Answer 1

The correct option is D $x^{77/15}$

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

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

$x^{(3/2+5/3-3/5+77/30)}$

$\Rightarrow x^{(\frac{45+50+8}{30}+\frac{77}{30})}$

$\Rightarrow x^{77/15}$