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} √(a)=a^{(1)/(2)}, \\ √(a)^n=a^{(n)/(2)}, \\ a^na^m=a^(nm). \end{gathered}`

Using the first and second properties we notice that:

`x^4y^5√(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}`