\((25)^{7.5}\times(5)^{2.5}\div(125)^{1.5}=5^?\)
Answer: B
Let \((25)^{7.5}\times(5)^{2.5}\div(125)^{1.5}=5^{x}.\)
Then, \(\frac{(5^{2})^{7.5}\times(5)^{2.5}}{(5^{3})^{1.5}}=5^{x}\)
\(\Rightarrow \frac{5^{(2\times7.5)}\times5^{2.5}}{5^{(3\times1.5)}}=5^x\)
\(\Rightarrow \frac{5^{15}\times5^{2.5}}{5^{4.5}}=5^x\)
\(\Rightarrow 5^{x}=5^{(15+2.5-4.5)}\)
\(\Rightarrow 5^{x}=5^{13}\)
\(\therefore x=13\)