Answer:
x^2(y^(1/3))^8 = OPTION (c)
Explanation:
Here are the steps to simplify the expression (x^3y^4)^(2/3) into simplest radical form:
Use the power rule for exponents, which states that (a^m)^n = a^(mn). Apply this rule to the exponent 2/3: (x^3y^4)^(2/3) = x^(32/3)y^(42/3)
Simplify the exponents: x^2y^(8/3)
To express the exponent 8/3 as a radical, first rewrite it as a fraction with a numerator of 8 and a denominator of 3: 8/3 = 2 2/3
Use the radical rule for exponents, which states that a^(m/n) = (nth root of a)^m. Apply this rule to the expression y^(2 2/3): y^(2 2/3) = (y^(1/3))^8
Combine the simplified expressions for x and y: x^2(y^(1/3))^8 = x^2y^(8/3)
This is the simplest radical form of the expression.
So, (x^3y^4)^(2/3) simplifies to x^2y^(8/3), which can be expressed in simplest radical form as x^2(y^(1/3))^8.