Question

What expression is equivalent to (x^4/3x^2/3)^1/3?

Answer 1

`\large\boxed{x^(4)/(3)}`

Explanation:

`\left(x^(4)/(3)x^(2)/(3)\right)^(1)/(3)\qquad\text{use}\ a^na^m=a^(n+m)\\\\=\left(x^{(4)/(3)+(2)/(3)}\right)^(1)/(3)=\left(x^(6)/(3)\right)^(1)/(3)=(x^2)^(1)/(3)\qquad\text{use}\ (a^n)^m=a^(nm)\\\\=x^{(2)\left((2)/(3)\right)}=x^{(4)/(3)}`