Question

$\frac{\sqrt{x}\cdot x^{\frac{7}{6}}\cdot x}{\sqrt[3]{3x}}$
If the above expression can be written as $x^n$, what is the value of $n$?

• A. $\frac{7}{3}$
• B. $2$
• C. $\frac{8}{3}$
  
• D. $\frac{5}{3}$

Answer 1

The correct option is A $\frac{7}{3}$

$a^m\times a^n=a^{(m+n)}$

$a^m÷a^n=a^{(m-n)}$

Using the above identities, we have

$\frac{\sqrt{x}.x^{\frac{7}{6}}.x}{\sqrt[3]{3x}}=x^{(\frac{1}{2}+\frac{7}{6}+1-\frac{1}{3})}$

$=x^{\left(\frac{3+7+6-2}{6}\right)}$

$=x^{\left(\frac{14}{6}\right)}$

$=x^{\left(\frac{7}{3}\right)}$

Thus, $n=\frac{7}{3}$