Answer:
[tex]x^\frac{8}{3} y^\frac{16}{3}[/tex]
Step-by-step explanation:
Given the expression [tex](x^4y^8)^\frac{2}{3}[/tex], to simplify the expression using the rational exponents;
Applying one of the law of indices to simplify the expression;
[tex](a^m)^n = a^{mn}[/tex]
[tex](x^4y^8)^\frac{2}{3}\\\\= (x^4)^\frac{2}{3} * (y^8)^\frac{2}{3}\\\\= x^{4*\frac{2}{3} } * y^{8*\frac{2}{3} }\\\\= x^\frac{8}{3} * y^\frac{16}{3}\\ \\The \ final \ expression \ will \ be \ x^\frac{8}{3} y^\frac{16}{3}[/tex]
