Solve: $( \frac{( 2^{5})^{2} \times 7^{3}}{8^{3} \times 7})$.

Given: Expression: $( \frac{( 2^{5})^{2} \times 7^{3}}{8^{3} \times 7})$.

To do: To solve the given expression.

Solution:

Given expression: $( \frac{( 2^{5})^{2} \times 7^{3}}{8^{3} \times 7})$

$=\frac{2^{5\times2}\times7^3}{( 2^3)^{3}\times7}$

$=\frac{2^{10}\times 7^3}{2^9\times7}$                  [$\because ( a^m)^n=a^{mn}$]

$=2^{10-9}\times7^{3-1}$                              [$\because \frac{a^m}{a^n}=a^{m-n}$

$=2^1\times7^1$

$=14$

Thus, $( \frac{( 2^{5})^{2} \times 7^{3}}{8^{3} \times 7})=14$