Question

Simplify the radicals. Assume that all variables can be any real number.

So I’m not too sure how to do this one... If anyone could give me an in-depth step by step solution it would help me out greatly!

Answer 1

`\sqrt[3]{(-27x^9)/(64y^(12))}`

we take cube root separately

`\sqrt[3]{-27} =\sqrt[3]{-3*-3*-3} =-3`

We know cuberoot (x^3) is x

`\sqrt[3]{x^9}=\sqrt[3]{x^3*x^3*x^3}=x*x*x= x^3`

`\sqrt[3]{64} =\sqrt[3]{4*4*4}= 4`

`\sqrt[3]{y^(12)} =\sqrt[3]{y^3*y^3*y^3*y^3}= y*y*y*y= y^4`

`\sqrt[3]{(-27x^9)/(64y^(12))}=(-3x^3)/(4y^4)`