Question

Evaluate is not clear

Answer 1

$\purple{ \huge{ \underline{ \overline{ \mid{ \bold{ \: \: QUESTION \: \: \mid}}}}}}$



$\boxed{\bold{ EVALUATE \: : \: \: \: \: \: \: \: \frac{6 {}^{3} \times 5 {}^{4} \times 3 {}^{2} }{25 \times 2 {}^{3} \times 9 {}^{2} } }}$



$\purple{ \huge{ \underline{ \overline{ \mid{ \bold{ \: \: SOLUTION \: \: \mid}}}}}}$



$\bold{ \frac{6 {}^{3} \times 5 {}^{4} \times 3 {}^{2} }{25 \times 2 {}^{3} \times 9 {}^{2} } } \\ \\ \bold{ = \frac{(2 \times 3) {}^{ 3} \times 5 {}^{4} \times 3 {}^{2} }{(5) {}^{2} \times 2 {}^{3} \times (3 {}^{2} ) {}^{2} } } \\ \\ \bold{ = \frac{2 {}^{3} \times 3 {}^{3} \times 5 {}^{4} \times 3 {}^{2} }{5 {}^{2} \times 2 {}^{3} \times 3 {}^{4} } } \\ \\ \bold{ = \frac{3 {}^{3} \times 3 {}^{2} \times 5 {}^{4} }{3 {}^{4} \times 5 {}^{2} } } \\ \\ \bold{ = \frac{3 {}^{(3 + 2)} \times 5 {}^{4} }{3 {}^{4} \times 5 {}^{2} } } \\ \\ \bold{ = \frac{3 {}^{5} \times 5 {}^{4} }{3 {}^{4} \times 5 {}^{2} } } \\ \\ \bold{ = \frac{3 {}^{5} }{3 {}^{4} } \times \frac{5 {}^{4} }{5 {}^{2} } } \\ \\ \bold{ = 3 {}^{(5 - 4)} \times 5 {}^{(4 - 2)} } \\ \\ \bold{ = 3 {}^{1} \times 5 {}^{2} } \\ \\ \bold{ = 3 \times 25} \\ \\ \bold{ = 75}$



$\purple{ \huge{ \underline{ \overline{ \mid{ \bold{ \: \: ANSWER\: \: \mid}}}}}}$ ➡


$\purple{ \huge{ \underline{ \overline{ \mid{ \bold{ \boxed{ \red \: 75} \mid}}}}}}$

Answer 2

$\begin{lgathered}\bold{ \frac{6 {}^{3} \times 5 {}^{4} \times 3 {}^{2} }{25 \times 2 {}^{3} \times 9 {}^{2} } } \\ \\ \bold{ = \frac{(2 \times 3) {}^{ 3} \times 5 {}^{4} \times 3 {}^{2} }{(5) {}^{2} \times 2 {}^{3} \times (3 {}^{2} ) {}^{2} } } \\ \\ \bold{ = \frac{2 {}^{3} \times 3 {}^{3} \times 5 {}^{4} \times 3 {}^{2} }{5 {}^{2} \times 2 {}^{3} \times 3 {}^{4} } } \\ \\ \bold{ = \frac{3 {}^{3} \times 3 {}^{2} \times 5 {}^{4} }{3 {}^{4} \times 5 {}^{2} } } \\ \\ \bold{ = \frac{3 {}^{(3 + 2)} \times 5 {}^{4} }{3 {}^{4} \times 5 {}^{2} } } \\ \\ \bold{ = \frac{3 {}^{5} \times 5 {}^{4} }{3 {}^{4} \times 5 {}^{2} } } \\ \\ \bold{ = \frac{3 {}^{5} }{3 {}^{4} } \times \frac{5 {}^{4} }{5 {}^{2} } } \\ \\ \bold{ = 3 {}^{(5 - 4)} \times 5 {}^{(4 - 2)} } \\ \\ \bold{ = 3 {}^{1} \times 5 {}^{2} } \\ \\ \bold{ = 3 \times 25} \\ \\ \bold{ = 75}\end{lgathered}$