Question

3√y^2=6√x y=n√x

Find n​

Answer 1

n = 4

Explanation:

Given equation:

`\sqrt[3]{y^2} =\sqrt[6]{x}`

`\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{(1)/(n)}:`

`\implies y^{(2)/(3)}=x^{(1)/(6)`

Take both sides of the equation to the power of ³/₂:

`\implies \left(y^{(2)/(3)}\right)^(3)/(2) =\left(x^{(1)/(6)\right)^(3)/(2)`

`\textsf{Apply exponent rule} \quad (a^b)^c=a^(bc):`

`\implies y^{(2)/(3) \cdot (3)/(2)}=x^{(1)/(6) \cdot (3)/(2)}`

Simplify:

`\implies y^{(6)/(6)}=x^{(3)/(12)`

`\implies y^1=x^{(1)/(4)`

Apply exponent rule a¹ = a :

`\implies y=x^{(1)/(4)`

`\textsf{Apply exponent rule} \quad a^{(1)/(n)}=\sqrt[n]{a}:`

`\implies y=\sqrt[4]{x}`