Discussion Forum

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

Answer:

Explanation:

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

Then, $\frac{(25)^{7.5} \times (5)^{2.5}}{(5^{3})^{1.5}} = 5^{x}$

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

$\Leftrightarrow \frac{5^{15} \times 5^{2.5}}{5^{4.5}}$

$\Leftrightarrow 5^{x}$
$= 5^{(15+2.5-4.5)} = 5^{13}$
$\Leftrightarrow x = 13$