Express each of the following powers of rational numbers as a rational number:
a. $ \left(\frac{-3}{5}\right)^{5} $
b. $ \left(\frac{4}{7}\right)^{2} $
C. $ \left(\frac{-3}{11}\right)^{3} $
d. $ \quad\left(\frac{7}{9}\right)^{4} $

To find:  We have to express each of the following powers of rational numbers as a rational number.

Solution:

a) $(\frac{-3}{5})^{5} = \frac{-3\times3\times3\times3\times3}{5\times5\times5\times5\times5} = \frac{-243}{3125} $

b) $(\frac{4}{7})^{2}$  = $\frac{4\times4}{7\times7}$ = $\frac{16}{49}$ 

c) $(\frac{-3}{11})^{3}$ = $\frac{-3\times-3\times-3}{11\times11\times11} = \frac{-27}{1331}$ 

d)$(\frac{7}{9})^{4} = \frac{7\times7\times7\times7}{9\times9\times9\times9} = \frac{2401}{6561}$