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Problem Simplify each of the following and express each as a rational number:
a. ( 3 2 ) 4 × ( 1 5 ) 2 \left(\frac{3}{2}\right)^4 \times \left(\frac{1}{5}\right)^2 ( 2 3 ) 4 × ( 5 1 ) 2
b. ( − 2 3 ) 5 × ( − 3 7 ) 3 \left(\frac{-2}{3}\right)^5 \times \left(\frac{-3}{7}\right)^3 ( 3 − 2 ) 5 × ( 7 − 3 ) 3
c. ( − 1 2 ) 5 × 2 3 × ( 3 4 ) 2 \left(\frac{-1}{2}\right)^5 \times 2^3 \times \left(\frac{3}{4}\right)^2 ( 2 − 1 ) 5 × 2 3 × ( 4 3 ) 2
d. ( 2 3 ) 2 × ( − 3 5 ) 3 × ( 7 2 ) 2 \left(\frac{2}{3}\right)^2 \times \left(\frac{-3}{5}\right)^3 \times \left(\frac{7}{2}\right)^2 ( 3 2 ) 2 × ( 5 − 3 ) 3 × ( 2 7 ) 2
e. { ( − 3 4 ) 3 − ( − 5 2 ) 3 } × 4 2 \left\{\left(\frac{-3}{4}\right)^3 - \left(\frac{-5}{2}\right)^3\right\} \times 4^2 { ( 4 − 3 ) 3 − ( 2 − 5 ) 3 } × 4 2
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