Discussion

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

Answer: B

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

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

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

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

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

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

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