Question

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. (x4y8)2/3

Answer 1

`x^(8)/(3) y^(16)/(3)`

Explanation:

Given the expression
`(x^4y^8)^(2)/(3)`, to simplify the expression using the rational exponents;

Applying one of the law of indices to simplify the expression;

`(a^m)^n = a^(mn)`

`(x^4y^8)^(2)/(3)\\\\= (x^4)^(2)/(3) * (y^8)^(2)/(3)\\\\= x^{4*(2)/(3) } * y^{8*(2)/(3) }\\\\= x^(8)/(3) * y^(16)/(3)\\ \\The \ final \ expression \ will \ be \ x^(8)/(3) y^(16)/(3)`