Question

What is the simplest radical form of the expression?

(8x^7y^4)^2/3


1. 8x4y3y√

2. 8x4y2x2y2‾‾‾‾√3

3. 4x10y6x√

4. 4x4y2x2y2‾‾‾‾√3 <<<<<<-----

Answer 1

`~~\left(8x^7y^4\right)^(\tfrac 23)\\\\=\left[ \left(8x^7y^4\right)^2 \right]^(\tfrac 13) \\\\=\left(64x^(14)y^8 \right)^(\tfrac 13)\\\\=\left(64 \right)^(\tfrac 13) \cdot \left( x^(14) \right)^(\tfrac 13) \cdot \left(y^8 \right)^(\tfrac 13)\\\\=\left(4^3 \right)^(\tfrac 13) \cdot \left(x^(12)\cdot x^2\right)^(\tfrac 13) \cdot \left(y^6 \cdot y^2 \right)^(\tfrac 13)\\\\=4 x^4 \cdot \left(x^2 \right)^(\tfrac 13) \cdot y^2 \cdot \left(y^2 \right)^(\tfrac 13)\\\\`

`=4x^4y^2 \left(x^2 y^2 \right)^(\tfrac 13)\\\\=4x^4y^2 \sqrt[3]{x^2 y^2}`