Question

If the expression $\frac{\sqrt{x}\cdot x^{\frac{5}{6}}\cdot x}{\sqrt[3]{3x}}$ is simplified as $x^n$, then the value of $n$ is

Answer 1

The given equation is written as
$x^{\frac{1}{2}}.x^{\frac{5}{6}}.x^1.x^{\frac{-1}{3}}$
Applying the multiplying law of exponents.
Take LCM for the exponents, we get
=$\frac{1}{2}+\frac{5}{6}+1-\frac{1}{3}$
= $\frac{12}{6}=2$
So, $x^2=x^n$
The value of n is 2.