\((25)^{7.5} \times (5)^{2.5} \div (125)^{1.5} = 5?\)
Answer: B
Let \((25)^{7.5} \times (5)^{2.5} \div (125)^{1.5} = 5x.\)
Then, \(\frac{(5)^{7.5} \times (5)^{2.5}}{(5^{3})^{1.5}} = 5x \)
\(\Rightarrow \frac{5^{(2 \times 7.5)} \times (5)^{2.5}}{5^{(3 \times 1.5)}} = 5x\)
\(\Rightarrow \frac{5^{15} \times 5^{2.5}}{5^{4.5}} = 5x\)
\(\Rightarrow 5x = 5^{(15+2.5-4.5)} \)
\(\Rightarrow 5x = 5^{13}, \therefore x = 13\)