Simplify the following expression. Assume the variables represent nonnegative real numbers.
\[
\sqrt{98 a b^{11}}
\]

Step 1 ：Find the prime factorization of 98: \(98 = 2 \times 7 \times 7\)

Step 2 ：Simplify the expression: \(\sqrt{98ab^{11}} = \sqrt{2 \times 7 \times 7 \times a \times b^{11}}\)

Step 3 ：Separate the factors inside the square root: \(\sqrt{2 \times 7 \times 7 \times a \times b^{11}} = \sqrt{2} \times \sqrt{7} \times \sqrt{7} \times \sqrt{a} \times \sqrt{b^{11}}\)

Step 4 ：Simplify further: \(\sqrt{2} \times \sqrt{7} \times \sqrt{7} \times \sqrt{a} \times \sqrt{b^{11}} = \sqrt{2} \times 7 \times \sqrt{a} \times b^{\frac{11}{2}}\)

Step 5 ：Combine the constants and exponents: \(\sqrt{2} \times 7 \times \sqrt{a} \times b^{\frac{11}{2}} = 7\sqrt{2ab^{\frac{11}{2}}}\)

Step 6 ：The simplified expression is \(\boxed{7\sqrt{2ab^{\frac{11}{2}}}}\)