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

A. 8.5

B. 13

C. 16

D. 17.5

Correct Answer : B.

Let

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

T h e n, \frac{(5^{2})^{7.5} \times (5)^{2.5}}{{(5^{3})}^{1.5}} = 5 x

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

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

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

\Rightarrow 5^{x} = 5^{13}, ∴ x = 13 .

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