Question

√ is simplified to x4y5y√. What were the values of H and K in the original question?

Answer 1

To solve this problem, we will use the following properties of exponents:

$\begin{gathered} \sqrt{a}=a^{\frac{1}{2}}, \\ \sqrt{a}^n=a^{\frac{n}{2}}, \\ a^na^m=a^{nm}. \end{gathered}$

Using the first and second properties we notice that:

$x^4y^5\sqrt{y}=\sqrt{x^{2*4}y^{2*5}y}.$

Simplifying we get:

$\sqrt{x^8y^{10}y}.$

Finally, applying the last property, we get:

$\sqrt{x^8y^{11}}.$

Answer:

$\begin{gathered} H=8, \\ K=11. \end{gathered}$