Answer:
[tex]x = \sqrt{y}[/tex]
Step-by-step explanation:
[tex]x^{3/4 } = y^{3/8 }[/tex]
Note that
[tex]x^{3/4 } = \sqrt[4]{x^3}[/tex]
[tex]y^{3/8 } = \sqrt[8]{y^3}[/tex]
So,
[tex]\sqrt[4]{x^3} = \sqrt[8]{y^3}[/tex]
[tex]( \sqrt[4]{x^3} ) ^8= ( \sqrt[8]{y^3} )^8[/tex]
[tex]( \sqrt[4]{x^3} ) ^8= y^3[/tex]
Once
[tex]( \sqrt[4]{x^3} )^8 = (( \sqrt[4]{x^3} )^4)^2= (x^3)^2 = x^6[/tex]
[tex]x^6 = y^3[/tex]
[tex]x = \sqrt[6]{y^3}[/tex]
[tex]x = y^{3\cdot 1/6}[/tex]
[tex]x = y^{1/2}[/tex]
[tex]x = \sqrt{y}[/tex]
