Simplify each of the following and express each as a rational number:

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Problem

Simplify each of the following and express each as a rational number: (1)

\left(\frac{3}{2}\right)^4 \times \left(\frac{1}{5}\right)^2

(2)

\left(\frac{-2}{3}\right)^5 \times \left(\frac{-3}{7}\right)^3

(3)

\left(\frac{-1}{2}\right)^5 \times 2^3 \times \left(\frac{3}{4}\right)^2

(4)

\left(\frac{2}{3}\right)^2 \times \left(\frac{-3}{5}\right)^3 \times \left(\frac{7}{2}\right)^2

(5)

\left\{\left(\frac{-3}{4}\right)^3 - \left(\frac{-5}{2}\right)^3\right\} \times 4^2