Explanation:

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

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

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

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

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

$\Rightarrow 5^{x}$=5⁽¹³⁾

$\therefore$ x = 13.