To evaluate \((\frac{2}{5})^{-3}\), we can use the property of negative exponents, which states that \(a^{-n} = \frac{1}{a^n}\).
So,
\[ (\frac{2}{5})^{-3} = \frac{1}{(\frac{2}{5})^{3}} \]
Next, we calculate \((\frac{2}{5})^{3}\):
\[ (\frac{2}{5})^{3} = \frac{2^{3}}{5^{3}} = \frac{8}{125} \]
Now, substituting back, we find:
\[ (\frac{2}{5})^{-3} = \frac{1}{\frac{8}{125}} = \frac{125}{8} \]
Thus, the value of \((\frac{2}{5})^{-3}\) is \(\frac{125}{8}\).
The corresponding response is:
1258 (125 eighths).
1 answer