((1)/(5))^3 cdot((1)/(5))^2 cdot((1)/(25))^-4

To solve the expression \( \left(\frac{1}{5}\right)^{3} \cdot\left(\frac{1}{5}\right)^{2} \cdot\left(\frac{1}{25}\right)^{-4} \), we can use the properties of exponents.<br /><br />First, let's simplify each term separately:<br /><br />1. \( \left(\frac{1}{5}\right)^{3} = \frac{1}{5^3} = \frac{1}{125} \)<br />2. \( \left(\frac{1}{5}\right)^{2} = \frac{1}{5^2} = \frac{1}{25} \)<br />3. \( \left(\frac{1}{25}\right)^{-4} = \left(25\right)^{4} = 25^4 = 390625 \)<br /><br />Now, we can multiply these simplified terms together:<br /><br />\[ \frac{1}{125} \cdot \frac{1}{25} \cdot 390625 \]<br /><br />To multiply fractions, we multiply the numerators together and the denominators together:<br /><br />\[ \frac{1 \cdot 1 \cdot 390625}{125 \cdot 25 \cdot 1} = \frac{390625}{3125} \]<br /><br />Finally, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 625:<br /><br />\[ \frac{390625}{3125} = 125 \]<br /><br />Therefore, the correct answer is \( 125 \).