Question

What is the expression in radical form? (7x^3y^2)^27

Options:
A) 7x^81y^54
B) 14x^81y^54
C) 49x^81y^54
D) 196x^81y^54

Answer 1

The expression in radical form for (7x³y²)²⁷ is 7²⁷ * x^(327) * y^(227), which simplifies to 7²⁷ * x⁸¹ * y⁵⁴.

Step-by-step explanation:

To express the given expression (7x³y²)²⁷ in radical form, we apply the power property of exponents, which states that when an expression with an exponent is raised to another exponent, we multiply the exponents.

(7x³y²)²⁷ = 7²⁷ * x^(327) * y^(227)

Solving the exponents within the parentheses, we get: 7²⁷ * x⁸¹ * y⁵⁴

Therefore, the final result of the expression in radical form is 7²⁷ * x⁸¹ * y⁵⁴, which corresponds to option C) 49x^81y^54.