Use the Rules of Exponents to Simplify the Expression $\left(\frac{\mathrm{t}^{-6 / 7}}{\mathrm{~b}^{-2 / 3}}\right)^{4}\left(\mathrm{t}^{-1 / 6} \mathrm{~b}^{1 / 2}\right)^{-1}$

Multiple Choice

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.
- $\left(\frac{\mathrm{t}^{-6 / 7}}{\mathrm{~b}^{-2 / 3}}\right) ^{4}\left(\mathrm{t}^{-1 / 6} \mathrm{~b}^{1 / 2}\right) ^{-1}$

A) $\frac{b^{19 / 6}}{t^{151 / 42}}$

B) $\frac{\mathrm{t}^{137 / 42}}{\mathrm{~b}^{13 / 6}}$

C) $\frac{\mathrm{t}^{151 / 42}}{\mathrm{~b}^{19 / 6}}$

D) $\frac{\mathrm{b}^{13 / 6}}{\mathrm{t}^{137 / 42}}$