What is the value of (2/5)^−3

Responses
8/125
8 over 125
125/8
125 eighths
−125/8
negative 125 eighths
−8/125

1 answer

To compute \((\frac{2}{5})^{-3}\), we can use the property of exponents that states \(x^{-n} = \frac{1}{x^n}\).

So, we have:

\[ (\frac{2}{5})^{-3} = \frac{1}{(\frac{2}{5})^3} \]

Next, we need to calculate \((\frac{2}{5})^3\):

\[ (\frac{2}{5})^3 = \frac{2^3}{5^3} = \frac{8}{125} \]

Now, substituting this back into our equation:

\[ (\frac{2}{5})^{-3} = \frac{1}{\frac{8}{125}} = \frac{125}{8} \]

Thus, the value of \((\frac{2}{5})^{-3}\) is \(\frac{125}{8}\).

From the options provided, the answer is:

125/8.