Question

What were the values of H and K in the original question? H = 9, K = 81 H = 4, K = 10 H = 10, K = 82 H = 7, K = 19

Answer 1

To find the values of H and K, we need to write

`x^3y^9√(xy)`

into

`√(x^Hy^K)`

Note that

`\begin{gathered} x^3=√((x^3))^2=√(x^6) \\ \\ y^9=√((y^9)^2)=\sqrt{y^(18)} \end{gathered}`

From the question, we have

`\begin{gathered} x^3y^9√(xy)=x^3* y^9*√(xy) \\ x^3y^9√(xy)=√(x^6)*\sqrt{y^(18)}*√(xy) \\ x^3y^9√(xy)=\sqrt{x^6* y^(18)* x* y} \\ x^3y^9√(xy)=\sqrt{x^7y^(19)} \end{gathered}`

Therefore,

`\begin{gathered} H=7 \\ K=19 \end{gathered}`