(25) 7.5 x (5) 2.5 ÷ (125) 1.5 = 5 ? Options: A . &nbsp8.5 B . &nbsp13 C . &nbsp16 D . &nbsp17.5 E . &nbspNone of these

(25)7.5 x (5)2.5 ÷ (125)1.5 = 5?

Question

(25)^7.5 x (5)^2.5 ÷ (125)^1.5 = 5^?

Answer: Option B

Let (25)^7.5 x (5)^2.5 ÷ (125)^1.5 = 5^x.

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

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

$\frac{5^{15}\times5^{2.5}}{5^{4.5}}$ = 5^x

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

5^x = 5¹³

Therefore x = 13.

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