By using the properties of exponents, we will see that:
H = 8
K = 11.
What are the values of H and K?
We start with the relation:
[tex]\sqrt{x^H*y^K} = x^4*y^5*\sqrt{y}[/tex]
Notice that we can use the property:
[tex]x^n = \sqrt{x^{2n}}[/tex]
Then we can rewrite the right side of our relation as:
[tex]\sqrt{x^H*y^K} = x^4*y^5*\sqrt{y} = \sqrt{x^{2*4}}*\sqrt{y^{2*5}}*\sqrt{y} \\\\= \sqrt{x^8*y^{10}*y} = \sqrt{x^8*y^{11}}[/tex]
Then we can see that:
If you want to learn more about exponents:
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