ANSWER
2b
Step-by-step explanation
To simplify this expression, we have to apply some of the exponents' properties. First, the square root is a fractional exponent,

So we can rewrite the expression as,

Then, we can distribute the exponents into the multiplication,

In this problem,

Exponents of exponents are multiplied,

In this problem,
![2(a^2)^(1/2)(b^8)^(1/2)(a)^(-1)(b^3)^(-1)=2\cdot a^(2\cdot1/2)\operatorname{\cdot}b^{8\operatorname{\cdot}1/2}\operatorname{\cdot}a^(-1)\operatorname{\cdot}b^{3\operatorname{\cdot}(-1)}]()
Simplify if possible,
![2\cdot a^(2\cdot1/2)\operatorname{\cdot}b^{8\operatorname{\cdot}1/2}\operatorname{\cdot}a^(-1)\operatorname{\cdot}b^{3\operatorname{\cdot}(-1)}=2\cdot a^1\operatorname{\cdot}b^4\operatorname{\cdot}a^(-1)\operatorname{\cdot}b^(-3)]()
Now, the product of two powers with the same base is equal to the base raised to the sum of the exponents,

In this problem,
![2\cdot a^1\operatorname{\cdot}b^4\operatorname{\cdot}a^(-1)\operatorname{\cdot}b^(-3)=2\cdot a^(1-1)\operatorname{\cdot}b^(4-3)]()
Solve the subtractions,
![2\cdot a^(1-1)\operatorname{\cdot}b^(4-3)=2\cdot a^0\cdot b^1=2b]()
Hence, the simplified expression is 2b.