Discussion

\((25)^{7.5}\times(5)^{2.5}\div(125)^{1.5}=5^?\)

Answer: B

Let \((25)^{7.5}\times(5)^{2.5}\div(125)^{1.5}=5^x\)

Then, \(\frac{(5^{2})^{7.5}\times (5)^{2.5}}{(5^{3})^{1.5}}=5^x\)

\(\Rightarrow \frac{5^{(2\times7.5)}\times5^{2.5}}{(5^{3\times1.5})}=5^x\)

\(\Rightarrow \frac{5^{15}\times5^{2.5}}{5^{4.5}}=5^x\)

\(\Rightarrow 5^{x}=5^{(15+2.5-4.5)}\)

\(\Rightarrow 5^{x}=5^{13}\)

\(\therefore x=13\)

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