# Evaluate:

Question:

Evaluate:

(i) $\left(\frac{5}{3}\right)^{2} \times\left(\frac{5}{3}\right)^{2}$

(ii) $\left(\frac{5}{6}\right)^{6} \times\left(\frac{5}{6}\right)^{-4}$

(iii) $\left(\frac{2}{3}\right)^{-3} \times\left(\frac{2}{3}\right)^{-2}$

(iv) $\left(\frac{9}{8}\right)^{-3} \times\left(\frac{9}{8}\right)^{2}$

Solution:

(i) $\left(\frac{5}{3}\right)^{2} \times\left(\frac{5}{3}\right)^{2}=\left(\frac{5}{3}\right)^{4}=\frac{5^{4}}{3^{4}}=\frac{625}{81}$

(ii) $\left(\frac{5}{6}\right)^{6} \times\left(\frac{5}{6}\right)^{-4}=\left(\frac{5}{6}\right)^{(6+(-4))}=\left(\frac{5}{6}\right)^{(6-4)}=\left(\frac{5}{6}\right)^{2}=\frac{5^{2}}{6^{2}}=\frac{25}{36}$

(iii) $\left(\frac{2}{3}\right)^{-3} \times\left(\frac{2}{3}\right)^{-2}=\left(\frac{2}{3}\right)^{(-3-2)}=\left(\frac{2}{3}\right)^{-5}=\left(\frac{3}{2}\right)^{5}=\frac{3^{5}}{2^{5}}=\frac{243}{32}$

(iv) $\left(\frac{9}{8}\right)^{-3} \times\left(\frac{9}{8}\right)^{2}=\left(\frac{9}{8}\right)^{(-3+2)}=\left(\frac{9}{8}\right)^{-1}=\frac{8}{9}$