Question

Simplify the expression.

Answer 1

C

Step-by-step 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.

Answer 2

we have

`\sqrt[4]{768x^(8)y^(5)}`

we know that

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

`768=2^(8) *3`

`({768x^(8)y^(5))^{(1)/(4)}=({2^(8)3x^(8)y^(5))^{(1)/(4)}`

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

therefore

the answer is the option C

`4x^(2)y\sqrt[4]{3y}`