What is the value of (2/5)^(-3) ?

A. 8/125
B. -125/8
C. -8/125
D. 125/8

1 answer

To evaluate \((2/5)^{-3}\), we can use the property of exponents that states \(a^{-n} = \frac{1}{a^n}\). Hence, we have:

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

Next, we need to calculate \((2/5)^3\):

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

Now substituting back into our expression, we get:

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

Thus, the value of \((2/5)^{-3}\) is:

\[ \boxed{125/8} \]

So, the correct answer from the options is D. 125/8.