Hello,I'm trying to simplify the following expression.

Question

√(4a^3*b^-6*x^2)/16a^-3*2b*x^-4)  

It's all under the square root sign.The final answer I got was: 64x^8/3b^7/2

But I have no clue if this is correct or not.

Answer 1

√(4/16*2)√(a³/a^-3)√(b^-6/b)√(x²/x^-4)

√(1/8)√(a⁶)√(b^-7)√(x⁶)

(1/2)√(1/2)(a³)(b^-3)√(b^-1)(x³)

(a³x³/2b³)√(1/2b)

√(1/2b)=1/√(2b)=√(2b)/2b

(a³x³/2b³)(√(2b)/2b becomes...

a³x³√(2b)/4b⁴