Question

I need help with this asap please

Answer 1

`y=(4)/(3)`

Explanation:

To determine the value of y for the given equation, use the exponent rules.

Given equation:

`\frac{\sqrt[3]{x^8}}{\left(x^4\right)^{(1)/(3)}}=x^y,\;\;x > 1`

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

`\implies \frac{\left(x^8\right)^{(1)/(3)}}{\left(x^4\right)^{(1)/(3)}}=x^y`

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

`\implies \frac{x^{(8)/(3)}}{x^{(4)/(3)}}=x^y`

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

`\implies x^{\left((8)/(3)-(4)/(3)\right)}=x^y`

Subtract the numbers:

`\implies x^{(4)/(3)}=x^y`

`\textsf{Apply the exponent rule:} \quad a^(f(x))=a^(g(x)) \implies f(x)=g(x)`

`\implies (4)/(3)=y`