ข้อสอบคณิต O-NET - 2551

$$\begin{gathered} \mathrm{จากโจทย์} {\left(\sqrt{\frac{8}{125}}\right)}^4={\left(\frac{16}{625}\right)}^{\frac{1}{x}} \mathrm{เป็นสมการ} Expo \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{จึงต้องทำฐานให้เท่ากันและจับเลขชี้กำลังมาเท่ากัน} \\ \mathrm{จะได้} \end{gathered}$$

$$\begin{gathered} {\left(\sqrt{\frac{2^3}{5^3}}\right)}^4 = {\left(\sqrt{\frac{2^4}{5^4}}\right)}^{\frac{1}{x}} \\ {\left(\frac{2^3}{5^3}\right)}^{\frac{4}{2}} = {\left(\frac{2^4}{5^4}\right)}^{\frac{1}{x}} \\ {\left(\frac{2}{5}\right)}^{\frac{\left(3\right)\left(4\right)}{2}} = {\left(\frac{2}{5}\right)}^{\frac{4}{x}} \\ \frac{\left(3\right)\left(4\right)}{2} = \frac{4}{x} \end{gathered}$$

$\mathrm{ดังนั้น} x = \frac{\left(4\right)\left(2\right)}{\left(3\right)\left(4\right)} = \frac{2}{3}$