Question

Simplify the expression.

Answer 1

we have

$\sqrt[4]{768x^{8}y^{5}}$  

we know that

$\sqrt[4]{768x^{8}y^{5}}=({768x^{8}y^{5})^{\frac{1}{4}}$  

$768=2^{8} *3$

$({768x^{8}y^{5})^{\frac{1}{4}}=({2^{8}3x^{8}y^{5})^{\frac{1}{4}}$

$({2^{8}3x^{8}y^{5})^{\frac{1}{4}}=2^{2} x^{2}y (3y)^{\frac{1}{4}}=4x^{2}y\sqrt[4]{3y}$

therefore

the answer is the option C

$4x^{2}y\sqrt[4]{3y}$

Answer 2

Answer

C

Explanation

⁴√(768x⁸y⁵)  = (768x⁸y⁵)¹/⁴

                     =768¹/⁴ × x⁸ˣ¹/⁴ × y⁵ˣ¹/⁴

⁴√768 = ⁴√(3 × 256)

            = 4 ⁴√3

x⁸ˣ¹/⁴  = x²

 y⁵ˣ¹/⁴ =  (y⁴ × y¹)¹/⁴

            = y⁴ˣ¹/⁴ ×  y¹/⁴

          = y ×  y¹/⁴

∴⁴√(768x⁸y⁵)  = (768x⁸y⁵)¹/⁴

                        = 4x²y  ⁴√(3y)

The answer is C.